Will it kill my tree?

It's not your tree, tell your landlord to cut *his* tree however he sees fit.

Cut it to 3 feet so that you can work more easily with it. Do this in the spring after the threat of frosts. (Do it now if your landlord is really insistent; do not wait until autumn.)

It will resprout from the stump. After a year (the next spring, after frosts), select one sprout and remove the others. Cut the stump again, this time slanting down from about 6 inches above the saved sprout. In three more years, you won't know it was cut. About three years after that, you will have to cut it down again to 3 feet.