Key questions/comments:
1) Was the mowing being done on private or public property?
2) Do you know the name (and address?) of the mowing service?
3) Take good, legible pictures of the damage.
4) Get estimates (at least two).
Now, with that information at hand, do the following:
a) If the mowing was on private property, contact the property owner in writing (see below). The mowers were operating as an agent of the owner and, depending on the specifics, the owner could be liable for the damage. If on public property, that is a big problem since most municipalities are protected.
b) Also, send a copy of your letter to the mowing service (if known). Both of your letters should include the details of your claim, a copy of the lower estimate, and a 'deadline' for response (5 days after receipt). Send both letters Certified RRR.
c) If you do not get satisfaction from the letters, you will have all the ammo you need to pursue a claim in Small Claims court.