  In this paper, we prove the existence of mean curvature flow with surgery for
mean-convex surfaces with free boundary. To do so, we implement our recent new
approach for constructing flows with surgery without a prior estimates in the
free boundary setting. The flow either becomes extinct in finite time or for
$t\to\infty$ converges smoothly in the one or two sheeted sense to a finite
collection of stable connected minimal surfaces with empty or free boundary (in
particular, there are no surgeries for $t$ sufficiently large). Our free
boundary flow with surgery will be applied in forthcoming work with Ketover,
where we will address the existence problem for $3$ free boundary minimal disks
in convex balls.
