Your nine points must be [**EDIT: very**] general [see MP's answer], otherwise it <i>can</i> be semiample.

The only effective anticanonical divisor is then (the strict transform of) the cubic C through the nine points. Since there is no other cubic curve cutting C in your nine points, the restriction of -K_S to C is a noneffective divisor of degree 0 (C has genus 1). So the restriction of -mK_S is also noneffective for all m (the points are general in C! I guess torsion points can make a difference) which means the only effective divisor in -mK_S is mC. Thus -mK_S is never base point free.