am I supposed to cut off the dead flowers to have them re-grow or do I leave them there?

You can trim them back JoEllen. You MAY get a few more blooms. Monarda, as a general rule, don't re-bloom very reliably. When mine are finished I usually end up trimming the plant right back to the ground. It will send up some new leaves and end up looking much tidier.

I tend to give mine a light trim and take all the dead flowers off. but as gilli says i dont tend to get new flowers either.

I don't trim mine back, they bloom beautifully and when they are finished I just cut them back. But we are in Alaska so by the time they finish blooming it is almost time to start cutting back the garden. Perennials

I trim off the dead flowers to the next shoots down and leave it, rather than completely pruning back the plant as its still green after dead heading and therefore prducing food for itself.