the screw is probably seized into the outer caliper half (which is, unlike the other half, threaded to accept the screw).
If this were my bike I would get someone to put a blob of MIG weld onto the screw head. The heat will free the seized screw threads, and you will have something to grip/swing on/grind a slot in. There are lots of other ways of addressing this issue, but that is the one that will work most reliably and most quickly IME.
The screw is listed separately as a spare part;
http://si.shimano.com/pdfs/ev/EV-BR-RS785-3743.pdfTo avoid a repeat performance
- use a screwdriver that fits the slot
exactly and push it firmly into the slot when undoing it. This can make about x10 difference to the torque that can be exerted before the screw is damaged in any way.
- put a little copper-ease on the screw threads when reassembling
- don't overtighten the screw; there is no need, bearing in mind that there is also a retaining clip on the back of the screw
hth
cheers