The earlier you cut, the more protien but the less tons per cutting. If you want to feed rabbits or dairy, cut before you see any blossoms.
If you are feeding cattle or meat animals, you might want more roughage/tons per cutting, and want to cut at 10% blooms. Hate to get later than that. (You will, when it rains.....)
Can lay a mower bar on the ground & cut, comes back fine. Shortness isn't an issue 'here'.
You shouldn't cut alfalfa between 200 & 600 growing degree days before the killing frost.
What does that mean you ask? :) During it's heavy growing period alfalfa pulls it's roots about empty of nutrition. Really bad to cut it off then & let it freeze up, empty for the winter. Very easy to winter kill then.
So, give it 20-30 days to grow be4 it freezes. However, once it freezes, you _can_ harvest that last cutting. But you'd like some snow cover, & short cut doesn't leave much snow cover. Depends where you are, for snow & how cold is cold.
Dairy folks here want 4 cuttings, high in protien. Cattle folks take 3 cuttings, little less protien. Both get about the same tons maybe. More protien for the dairy, less machine/labor costs for meat. You can play with alfalfa a bit.