Assuming; 1) You are trying to keep long stock fully supported while cutting. 2) You do not want to move the stands.

Even if you swivel the whole saw, you still have to swivel the vise if you are going to use it to hold the stock. Mount the saw on a turntable what pivots around the same point the saw vise pivots around. That way when you pivot the saw, the vise will stay in the same position. You will just have to adjust it to match the new angle of saw.