2001 saturn sc1 grinds when going into third gear

clutch not properly disengaging
if old clutch , check cable/hydraulics
air in system or broken clutch cable
if new clutch kit fitted pull the transmission again and turn the clutch plate around as the hub springs are hitting on the flywheel bolts

loosen the line at the master cylinder to allow the master cylinder to prim properly then bleed out the system. There is still air in the system.

The clutch plate can only be fitted one way. If you noticed one side of the plate has a raised section that contains springs. The other side is flat. Puting the plate the wrong way round allows the raised section to hit the heads of the flywheel bolts and this is causing the clutch to spin even though you have the foot on the clutch. Make sure you have properly bled the air from the clutch system. Mostly there is a notice printed on the clutch plate which reads like flywheel side or this side away from flywheel

Sounds like the friction surface of the clutch disc is slipping. You would have to install a new clutch (clutch disc, pressure plate, and clutch release bearing), and have the flywheel surface cut and polished back to perfect smooth by a shop.
Manual transmission gears don't slip like automatics. And lack of fluid in the transaxle or the hydraulic clutch system won't cause this either.

Generally the clutch has failed to operate.
Could be the clutch disc, or the hydraulic system that moves it. Could even be the disc is stuck to the flywheel.
If the clutch master cyl is full of fluid, you may need a shop for repairs.

time has come to pay someone to pull the motor out and replace the clutch, do all the clutch components and resurface the flywheel. If the pedal is up then you do not have an actuator/hydraulic failure, your problem lies within the bellhousing. do some research for clutch kits, i have seen several on ebay for less than a hundred bucks. labor is not going to be cheap.

If the gears grind when engaging at standstill, the clutch is not breaking. The possible reason for this in order of probability are...
1. Air in the hydraulics . Caused by leaking slave cylinder, which would have to be overhauled, new kit fitted bled and adjsuted.

2. Clutch adjustment, either cable or pushrod if hydraulic.

3. Clutch assy worn out and requires replacement with full clutch kit.May also require machining the flywheel.

If your able to shift with the car off sitting in your driveway but not able to shift once the engine is running then you have one of several possible problems.

Problem 1) Possible clutch hydraulics problem where the hydraulics are not completely disengaging the clutch.

Problem 2) Clutch pressure plate fingers could be tired and not allowing the pressure plate to disengage the friction disc off the flywheel.

Problem 3) Not likely but depending on the abuse of the car, the synchros could be shot.

If the car has a decent amount of miles on it and is driven in the city a lot then Problem 1 and 2 are most likely the problem. So either way it's time to check some hydraulics or replace the clutch.

you will need the clutch checked over. the clutch hydraulic system is first to check. check fluid level, if its low, top it off with brake fluid, and find where its leaking. if the fluid is full, make sure the pedal feels normal.if its in the hydraulic system, the trans doesnt have to come out, but a clutch replacement it will....... does the clutch slip? if so it will need replacement. if noisy only when depressing the pedal, the throwout bearing, or pilot bearing may be bad, and clutch replacement will be needed. be sure to have the flywheel resurfaced and replace the rear main oil seal while the flywheel is off.

You have air in the hydraulic system, sometimes there is a funky bleeding routine. I hade a Ford Ranger and you had to pump up the clutch master cylinder before connecting it to the slave cylinder, it took a couple of tries but it did work in the end.