Giant slingshot made from 2" PVC. Cement insufficient. How to fasten for load?
I hate to be the bearer of bad news but 2" PVC will not handle the stress that a working slingshot goes through. The best fix for what you have would be under the comment Aloysius D mentioned about joining the top to the bottom with 45 degree braces. I think it would still want to roll backwards on you on the draw to use it. That's when it will fail at the joints where the vertical meets the base. The joint will be in tension as compared to rolling out of the tee connectors when there are no braces.

A good old fashioned tree limb in the shape you need bolted to a base and braced might be better, at least cheaper than one made of 2" threaded metal pipe.