I don't think it would be a good idea.
-Lightsabers can reach temperatures ranging from 18,000°C to 25,000°C
-A temperature as low as 300 ºC can lead to dry grass catching on fire
So, pretty good chance of just burning all the grass on your lawn, and your house to. But, lets say you can swing it fast enough so that there isn't enough time for the grass to catch fire, it still cuts the grass by burning it. So at the very least all the blades of grass would have black burned tips on them. I couldn't find any information on how damaging it is to grass health by cutting it with heat however, so I cannot say if doing this regularly would cause your grass to die.
But, I did find this video about a guy who decided to mow his lawn with a laser. You can see how damaging the heat is to the grass.
I actually really enjoyed In the Name of the King