Want to reroute a 2 inch copper vent pipe about 6 inches over that starts in the basement and goes up through the roof. Can I cut the copper pipe in two spots and use 2 inch pvc pipe, 2 pvc 90 degree elbows and rubber couplings to reroute the vent pipe?

I'm a DIYer and don't know too many codes, but I would say yes.
I do know that there are codes (national + by probably all 50 states) that limit what you can do with sections taken out of cast iron.

Of course I'm wondering if this is really just a vent rather than a drain + vent. It's venting just one thing, in the basement?

Yes, you can replace it with PVC or ABS pipe. Use proper Fernco coupling designed to connect Copper and PVC / ABS pipe as each has different Outside Diameter. Support new pipe within 6" of each connection to the joist with approved strap.

In some instances, all exposed pipes - including vents - are required to be metal. It is either from fire safety reasons or preventing them from being damaged by activity around them. If you still use PVC / ABS pipe, than you would have to soffit it in to comply with this regulation

Hope that helps

Milo