No, that's quite a stretch to call mineral exploitation a military purpose. It would at most be a strategic independence from other sources of minerals like China.

The other parts "permanent access" with "no approval needed" was part of the 1951 agreement. While I don't know the specifics on the independence of Greenland and what the old agreement said, I think Greenland didn't have the influence back then and it wasn't a matter to be discussed, so it might have been void in that case. But if Greenland goes independent they're basically up for grabs and Trump would be first in line.