Whenever we do force and acceleration problems, we normally
ignore air resistance.  The problem would be too complicated if
we tried to include it, and we don’t have enough information to
account for air resistance anyway.

But I think we’re going too far if we ignore water resistance for this
question.  The equation for Newton’s second law … F = M · a …
is talking about the NET force on an object.  I think we can all
agree that the 250 N of force with which the swimmer pushes
away from the wall is NOT the net force on the swimmer. 

As soon as the swimmer starts moving through the water, the water
resists the motion with a bunch of force.  The magnitude of the force
due to water resistance depends the swimmer’s size, shape, and posture,
plus what kind of swimsuit s/he’s wearing and how much hair s/he has.

The question doesn’t give us any of that information, and even if we
had it, it would take a team of hydraulic engineers to use it properly.
It’s certainly way over MY head.

So I’m going to say that this question can’t be answered as it’s written.

IF the 250 N were the total, NET of ALL forces acting on the swimmer,

         Acceleration  =  (force) / (mass)  =  (250 N) / (70 kg)

                                                         =        3.57 m/s² .

But you and I both know that it isn’t.