Do beetles eat spiders

nope. they eat bees, ants, etc. but not beetles.

An interesting bit of info

Tarantulas will stun a beetle or a wasp and lay eggs on it. The beetle or wasp stays alive but paralyzed and when the eggs hatch they eat the beetle or the wasp.

I thought that I'd add a little information to this answer. The user asking the question above did not specify Tarantulas or just any spider in general. There is a spider that primarily eat beetles it's fangs are specially designed to penetrate a beetles shell. I do not know the exact name of this spider. It's found in the western United States. If anyone does know the name of this particular spider please message me at my_life_notyours@live.com.