Over the years we, and I think everyone else that is a professional grass cutter, has messed up some lawns because it's been too wet.  Now we err on the side of no-mow vs. mow.  It's not worth the ruts.

We have made some bigtime messes, where the lawn mowers actually got stuck.  In those few occasions, we had to wait for the grass to dry out, and actually get new sod to replace the areas that we messed up.  Having to do a major repair is usually a rarity.

What I've realized, is that when you see, "ruts", it looks way worse than it really is.  What happens is the tires and the weight of the lawn mower will push the grass down.  If the ground is wet, then it gets the grass wet/muddy.  The solution is to spray the grass with the garden hose, and it cleans right up.  

If there is slight damage, vs. just mud on the grasss, you might have to step on the outer edges of the rut.  The act of doing this will, "fill the rut in".  Then a simple wash with the garden hose will make it perfect.

Now if a lawn mower gets stuck, and needs to be pulled out, well now you might be looking at fill dirt, and now sod. That's why we err on the side of no mow, and wait until next week.

No client has ever appreciated the, "effort", of rutting up the lawn when it's excessively wet, just to get the lawn cut, but everyone appreciates us waiting.

So that's what we do. :-)