Is there a mechanism for Trump to force Britain to recall the ambassador (deportation, etc..)
Yes, and he can even do so without taking much action. Indeed, the Vienna Convention offers an option that is an official action. Declaring the British ambassador persona non grata right after the leaking would certainly make headlines, likely alluding to the idea that Trump takes the leaks personally.
Instead, there's a much neater way to achieve the same outcome without much attention being drawn to the American side of the issue. The thing to keep in mind is that the British ambassador (or any ambassador and their staff) are there to represent the sending state's interest in the receiving state.
As president, mister Trump has the power to prevent an ambassador to the US from doing their job by making it clear to his officials that he doesn't like cooperation with this person.
In politics, this isn't new, indeed Wikipedia lists many examples of so-called cordons sanitaire. The term is commonly used to describe political parties which the other parties have agreed not to work with (on some level), that's a big problem for such a party as they are very much limited in passing the legislation they want. For an ambassador, however, this is much more of a problem as it's almost their sole job to to cooperate.
Indeed, tweets like these will do the job of setting such a cordon sanitaire, possibly aided by a written or verbal instruction to top-officials not work with them:
The wacky Ambassador that the U.K. foisted upon the United States is not someone we are thrilled with, a very stupid guy. He should speak to his country, and Prime Minister May, about their failed Brexit negotiation, and not be upset with my criticism of how badly it was...
...handled. I told @theresa_may how to do that deal, but she went her own foolish way-was unable to get it done. A disaster! I don’t know the Ambassador but have been told he is a pompous fool. Tell him the USA now has the best Economy & Military anywhere in the World, by far..
Indeed, it worked, from the Guardian:
In a shock move which prompted the senior civil servant at the Foreign Office to call an all-staff meeting to reassure “shaken” diplomats, Darroch announced on Wednesday he could no longer continue in his role following a leak of official cables in which he criticised Donald Trump.
The Guardian understands that he concluded he could not go on after he watched Tuesday’s Conservative leadership TV debate, where Johnson repeatedly dodged questions about whether he would sack the ambassador if he became PM.
Johnson is of course the front-runner in the Conservative leadership contest and it's likely he will be the next UK PM.