No, it gets cut if its attacked regardless of whether or not its supported.

OK, thanks

OK following conundrum: The attacker is trying to take St.P from the defender.
Defender has: A St.P, A Liv, A Mos
Attacker: A Fin, F Nor, F Bar, F Bal
and orders: A Fin - St.P, F Nor S A Fin - St.P, F Bar S A Fin - St.P, F Bal - Liv
could the Defender order: A Liv - St.P, A Mos S Liv - St.P, A St.P - Nor
Now I know that a defender can't cut a support that is meant to attack him
but in this case the conflict is between A Liv and A Fin. So is A St.P allowed to cut F Nor's support here?

sceptic_ka, StP doesn't cut Norway support because of the rule you mention and because StP doesn't dislodge Norway. The Livonia attack on StP doesn't affect the support cutting rule. StP is dislodged, Fin succeeds, Livonia doesn't move. The conflict isn't so much between Livonia and Fin, as involving all three units attempting to be in StP at the end of the move: Livonia, Fin and StP. A unit that is prevented from moving effectively attempts to hold its original province with strength of 1.