How do i fix a leak coming from the outside mirrors?

this sounds like the reflective material of the mirror coming off the glass. take it to a glass/mirror shop and see if they can just repair/replace the mirror glass with new reflective material.

what mirror? inside or side one??if the one outside than check if the hocks are still there,if broken(they need to hold the mirror) than the only solution before you spend money it is to buy a tube of external silicon or hot glue with the machine than apply some all around the board of the mirror(1 inch before the edge) than apply in the screen,hold it for few minutes and I hope it should be fine until you do not hit another car!
good luck!

Could have a DDS an PDS .depends on what RPO code yours has >
Outside Mirror Description and Operation (with RPO DL3)
Or
Outside Mirror Description and Operation (without RPO DL3)
Without
Heated Outside Rearview Mirror Operation
The REAR DEFOG relay controls the operation of the heated outside rearview mirrors. When rear window defogging is requested, the REAR DEFOG relay is energized and B+ is applied to the supply voltage circuit of the mirror heater element, located in the mirror face. A constant ground is also applied to the mirror face. Current will pass through the mirror heater element, warming the mirror, so long as the rear window defogger is commanded ON.

With
Heated Outside Rearview Mirror
The DDS and PDS control the activation of the mirror heaters. Upon receiving a serial data message indicating a request for heated mirrors, the DDS and PDS, will apply voltage to the mirror heater element supply voltage circuit. The mirror heaters will remain active until a new message is received indicating rear defogger is to be deactivated.
The power mirror system consists of the following components:
• Driver Door Switch (DDS)--An electronic control module with integrated switches and requires programming when replaced
• Passenger Door Switch (PDS)--An electronic control module with integrated switches, requires programming when replaced
• Power Mirror Direction Switch--Integrated into DDS and is a four position momentary switch that provides a signal input to the DDS for up, down, left/extend and right/retract with a mirror switch activation
• Mirror Select Switch--Integrated into DDS and is a three position switch that allows the operator to select the left or right mirror and also a neutral/fold position
• Mirror Extend/Retract Switch--Integrated into DDS and is a two position switch that allows the operator to select the mirror extend or mirror retract position
• Left Outside Power Mirror--Contains both the vertical and horizontal mirror motors
• Right Outside Power Mirror--Contains both the vertical and horizontal mirror motors
• Body Control Module--An electronic control module that requires programming when replaced, serves as the power mode master and is the main message handler
• Horizontal and Vertical Position Sensors, if equipped with memory mirrors--Supplied a 5-volt and low reference by the DDS/PDS and provide a variable voltage signal to the DDS/PDS that is proportional to mirror position
• Folding Mirror Motor, in each of the outside mirrors, if equipped with power fold mirrors--Provides extend and retract movements of the mirror and is serviced as a complete mirror assembly
Your best bet mite be to take to a qualified repair shop , i really don't think you'll be able to do anything with it.
Do you have wiring diagrams so you know which wires to test ,do you know how to do electrical testing ?
The Driver Door Switch (DDS) and Passenger Door Switch (PDS) supply voltage to the outside rearview mirror heater elements upon receipt of a serial data message from the HVAC module indicating that the rear defrost system is active. The door switch supplies B+ through the driver/passenger mirror heating element supply voltage circuit when a request is seen. Ground is applied through the driver/passenger mirror heating low reference circuit.

glass and motor availbable separately

Removal
NOTE: Do not remove the mirror assembly when repairing the individual mirror part. Individual mirror parts can be installed without removing the mirror assembly.

1. Remove the front door trim panel; refer to Section 501-05.

1. Remove the outside rear view mirror access water shield.

1. Remove the speaker.
   1. Remove the screws.
   1. Disconnect and remove the speaker.

1. Disconnect the outside rear view mirror electrical connector.

1. Remove the outside rear view mirror.
   1. Remove the nuts.
   1. Remove the outside rear view mirror.
      • Feed the outside rear view mirror wiring through the opening in the front door.

If the movement controls on the back of the mirror broke you will have to replace the entire mirror assembly. Go online to Rockauto.com and put in your car info and you will be able to select the mirror for your car. They are the least expensive place I have found for parts for do it yourself people who want to save money. Have used then for years for mirrors, headlights, fenders, hoods, etc.

here's 1996, all I have. Please rate.

Mirror, Power — Outside Rear View NOTE: This procedure applies to both RH and LH power outside rear view mirrors.

Removal

1. Remove the front door trim panel (23942). Refer to Section 01-05 for the removal procedure.
   

1. Remove the two outside rear view mirror inside mounting hole cover screws and the outside rear view mirror mounting hole cover (17K709) from the front door (20124).
   
   
   
   
   

1. Remove the wire clip.
   

1. Disconnect the power outside rear view mirror electrical connector.
   
   
   
   
   

1. Remove the three power outside rear view mirror bolts and the power outside rear view mirror.
   
   
   
   
   

Installation
To install, reverse the removal procedure. Tighten the three power outside rear view mirror bolts to 3-4 Nm (27-35 lb-in). Glass, Outside Mirror
Removal and Installation
Refer to the glass replacement procedures in Manual Mirror for power outside rear view mirror glass (17K707) Trim Cover
Removal

1. Remove the front door trim panel. Refer to Section 01-05 for the removal procedure.
   

1. Remove the two outside rear view mirror inside mounting hole cover screws.
   
   
   Remove the outside rear view mirror mounting hole cover.

Installation
To install, reverse the removal procedure. Mirror Control
Removal

1. Use a small flat-blade screwdriver to pry the power outside rear view mirror control switch from the instrument panel (04320).
   
   
   

I HAD THIS SAME PROBLEM AND IT WAS THE BYPASS HOSE THAT GOES INTO THE BACK OF THE WATERPUMP.IT IS AMETAL HOSE AND IS USUALLY ADEALER PART FOR ABOUT $70.00 THERE IS ALSO A O RING THAT COULD BE LEAKING.YOU NEED TO TAKE OFF THE INTAKE MANIFOLD TO GET TO IT.IT IS APRETTY EASY FIX TAKES ABOUT 2 HOURS.

1. Remove the front door trim panel (23942) ; refer to Section 501-05 .
   • Peel back the watershield.

1. Remove the rear view mirror mounting hole cover (17K709).

1. Disconnect the power mirror electrical connector.

1. Remove the outside rear view mirror (17682).
   1. Remove the screws.
   1. Remove the outside rear view mirror.

please rate as fixya if this works for you.

Same thing happened to mine.. i have a 97 skylark.. its coming from the heater core compartment under the dash.. most cars leak on the inside when the heater core blows.. but this car has a drain that leaks it outside under the passenger side... hope this helps.. G-LaL

open the door, on the opposite side of the mirror there is an interior panel, remove it, there are 3 nuts in there remove those, the mirror should come off, if it is power be sure to unplug it.