I noticed my neighbor cutting her flowers
Why is she cutting down her flowers?
I think she wants to kill them to free up space in her garden
It sounds like your neighbor is just taking care of her garden.  Some flowering plants actually live longer and grow stronger if they are carefully cut back at certain times of year.
Maybe she is just a mentally ill gardening enthusiast
I do not think that that makes her mentally ill. I think that she is just pruning them back so that the grow in thicker. It is good that she is maintaining her garden.