Mowing the grass in the rain can be miserable and without the correct equipment, you will not be doing the grass any favours either. Some commercial mowers such as the Mountfield S461 and the Hayter Motif 53 can handle the task; most residential lawn mowers aren't up to it. At best, you may end up with a badly cut lawn. At worst, you can end up with ruts and dead patches that are a pain to repair.
There are numerous of reasons why rain gives grass the upper hand when you try to mow, Grass behaves like people when it's getting rained on: it hunches over. The result is that many blades of grass get pushed over, not cut, when you try to mow. At least until the sun comes up, when all of the uncut grass should once again stand at attention. Some of the wet grass may stick to the mower blades, making it cut less efficiently.
Wet grass can stick to the mower's undercarriage, eventually getting thick enough to impede the mower blades and slow their rotation, further diminishing the mower's cutting ability.
Most mowers have mulching blades that create suction. Cut grass gets sucked up and cut into tiny pieces when it's dry. But when it's wet, the grass clumps up and doesn't get mulched.
If your grass has been saturated past its root depth, and if your mower wheels or shoes slide laterally, they can literally push the grass, roots and all, out of place, leaving ruts.
If you do decide to mow in the rain, make sure you are using a top of the range mower that is up the task.
