What type of glue is best for applying appliqué onto a satin clutch purse?
You run the risk of staining satin with any type of glue so if you use a glue you are going to have to be very careful not to let any seep out from under the edges of the appliqué. That said you can try Gripp glue.
You didn't say if this was a beaded appliqué or a lace appliqué but if you can your absolute best way to attach this is to hand sew it to the purse. Use a thin strong matching thread and take tiny stitches. It shouldn't take that long and then there is no chance of staining the satin.
Best of luck,