Can you drive a dump truck with a class a restriction license in Texas?

Yes, within the confines of what the restriction states. I'd need to know exactly what the restriction is for. If, say, it's an out-of-state license, and you have the intrastate only restriction, then you wouldn't be able to. If it's a restriction for something like having to wear glasses while driving, then you could, but you'd have to be wearing your glasses.