Trump certainly has the authority to cancel the deal (signed by Obama in November 2016 or not) after the fact - it has been done before. It is clearly an issue representing incoherence in his White House that he did not cancel the deal.
Mattis seems to be running things on his own, unsupervised or controlled by the White House. He also seems too deeply in bed with the Saudis and the Gulf States which are none of them our true friends, no matter what Iran is up to and no matter how much the Mullahs in Tehran will also never be our friends.
Leaving out the political and ideological angle, would Trump risk angering Boeing, Raytheon and hordes of other contractors (and their employees) by cancelling an approved deal?
Interestingly, it was the Qatari Defence Ministry that said this deal would create 60,000 jobs in 42 U.S. states. Imagine if the deal was cancelled: His rivals would say that Trump was acting tough with a very fringe player, while larger and more influential states (like the UAE and KSA) got away.