Does doing a burnout do any damage to my car? Yes, if done for too long your car can overheat. The transmission and clutch can overheat. If you have an automatic and you're holding the brake for too long, it will wear out.

Are burnouts bad for the clutch?

It of course is bad for the tires. It isn't great for the clutch but how bad depends on how fast the clutch is able to lock up.

What happens when you burnout a clutch?

If the clutch facings start to burn, the smell will resemble that of burnt toast. This could cause the whole clutch to fail, at which point your car would stop being able to accelerate or shift gears.