Not knowing that bleach was not to be used on Aida cloth, I tried to get some stains out by using bleach. now I'm afraid the counted cross stitch piece is ruined.
Is is possible to cut out a completed design from a ruined piece of aida cloth and put it on a clean piece of aida cloth?
If the bleach did not harm the stitching, you could do that. It might be easier and less risky to the finished piece if you framed it with fabric rather than attempting to cut it out. This would be easy if the piece is a square or rectangle, tricky if it is an odd shape. You would sew it to the top of the cloth sort of in place of a mat and miter the corners so it lies flat. If it is an odd shape, you will need to do it like a piece of applique.