How can I remove these screws from shutters?
Have you tried just pulling the screw?  If it is a plug anchor it should just pull right out with moderate force. If it is a toggle-like anchor (where something expands behind the wood), try pulling the screw until it feels tight, then hold the anchor with a pair of pliars and try turning the screw.

Worst case just cut the screw off with a pair of tin snips, a rotary tool with a cut-off wheel, etc. Once the screw head is off you can probably just push the rest of the screw and anchor into the void behind the wall.