Of course - the frame is aluminum, the stencil is stainless. If you cannot or don't want to do that your recycler might do that for you.
It took me a few minutes to disassemble a relatively large stencil, I only had to take off the tape and push the stencil down, the glue was still in-place attached to the frame, it could be hammered off.
We also process Aluminum with our CNC so we recycle Aluminum anyway from time to time. I'd say it's worth at least 1-2 coffees.
On the other side maybe the company which makes the framed stencil will take it back and make a new one out of it, talk with them if they're nearby. If you get the stencil from abroad, recycling is probably best.
I think 1kg Aluminum (chips from the CNC) is worth around 2.50$ (closest nearby), a little bit further I'd get a little bit more for it here. Block materials are worth more. New material for processing is around 5-6$ per kg.