If you remove your engines thermostat the engine will run cooler and over the short term it won't harm the engine but your heater may not work as good or at all without the engines thermostat.
The purpose of the engines thermostat is to keep the vehicles engine at the proper operating temperature and actually running a vehicles engine too cool can be damaging to the engine.
So if you need to remove a stuck thermostat that is stuck closed so you can drive it for awhile until you can get a new thermostat that is okay but you should get a new thermostat as soon as possible so that your engine will be able to operate at the correct temperatures to prolong your engines like.
Driving with a thermostat that is stuck open is okay but if your thermostat is stuck closed then it can cause your engine to overheat.