One of the basic mis-conceptions of evolutionary theory is that by altering a plant/animal after it has seeded/been born, you can somehow influence its evolution.
This is like saying if all humans had a leg chopped off at birth, eventually all humans would be born with only one leg. However, humans are genetically 'programmed' to have two legs, and no amount of chopping can alter that. It is only mutation that can alter our genetic make-up.
If grass to evolve into some self-cutting/shedding thing, it would have to be a result of a RANDOM mutation that bestowed some form of benefit to that individual above the others.
Grasses are already highly evolved, in that they grow from the base of the plant, (not the tips). This means if they are grazed by animals, they can continue to grow if their top has been eaten away. It is in the plants interest to be able to grow quickly and continually, as otherwise they would be grazed away completely, roots and all.
So, the short answer is 'No', as grasses have evolved to withstand grazing or mowing anyway. That's why we use them as 'lawns' in the first place!!