Use a suction cup to pull the screen away from the frame and create a small gap.

This should not require excessive force. Apply additional heat as needed to soften the screen adhesive.

Cover the screen with a layer of packaging tape if severe cracks or screen damage prevent a suction cup from obtaining a complete seal. The Galaxy S4 Mini also has enough of a gap between the frame and the screen to insert a jimmy or plastic opening pick. Carefully apply heat as needed, and wedge the screen free.