Can you cut up a t-shirt and reuse the design on something else like a quilt and sell that

yes, but... Yes, as long as you made the original design. If you did not, you will likely be sued for copyright infringement. If you purchase a T-shirt, the copyright owner of the design has no further right to regulate anything you do with it, as long as you do not make your own copies. On the other hand, some designs may also be protected as trademarks and that would be a different question.