My mixer is leaking oil.

This kind of unit are lubricated with grease paste. If the unit stays inactive for a long time, or if the motor and gears are overheating the grease paste gets melted into thin oil, and that will cause the leak.
The oil leak is usually coming from the gear box inside the appliance.
To fix the problem the unit must be taken apart, and cleaned. After this step, there is need to spread again the grease, using special foodsafe grease paste.
Disassemblying the gear box is not that easy, you will need previous experience and a gear puller to do the job properly and safely.
This appliances are also held with security screws to prevent the users from taking apart the unit, and can only be disassembled using a Security screwdriver tip.

The grease can be purchased here, check at the bottom of the page: Kenwood chef food mixer Grease.