A local police force doesn't magically become a military force, no matter what the mayor orders it to do any more than a man magically becomes a woman by putting on a dress. The local police force is bound to faithfully enforce the laws within their jurisdiction, any orders to the contrary are unlawful (no matter who gives them) and would likely (and justifiably) be ignored by any law enforcement agency.
The mayor can say what he wants as long as it's not the incitement of imminent violence (which this was not), if he actually starts issuing orders to his local police force contrary to its jurisdiction then that's another matter but he hasn't done that yet and unless he's gone completely insane never will.
It's all peacock posturing just like all these Blue State Governors false bravado, when push comes to shove, they all know the judicial branch will rule against them and that they own citizens are likely to turn on them if they fail to cooperate in getting the illegal immigration problem under control.