A special ops team made up of foreign soldiers as well as Americans do special ops missions across the world. until they are setup by their own government, forcing them to go into hiding.

Everything the others are saying here is on the money. If your story has a main character /protagonist, then your logline should be centered around him (or her). If it is a multi-protagonist type structure (think THE DIRTY DOZEN) rather than single-protagonist (think RAMBO), then you need to be aware of that and structure your logline a bit differently.

Who is your protagonist? Loglines work a certain way because they presuppose that your story is about one character trying to achieve one goal.

"When his team is setup (doing what?) by their own government, a tough as nails covert operative must (do what? How will he resolve this issue) before (what are the stakes)?"

The story you describe in your logline is about a conspiracy, and the action your protagonists take is to run away. Very unsatisfying. So your protagonist's goal either needs to be seeking out and exposing the head of this conspiracy, returning the world to balance that way. otherwise, I would suggest removing the conspiracy element - and make it a story about your characters escaping a situation.

Also ... what sets this apart from the Mission Impossible and Jason Bourne franchises? Even SWAT?

First: I would say, "multinational special ops team" instead of "a special ops team made up of foreign soldiers as well as Americans." (Plus if they are a special ops team you don't need to tell us they do special ops missions)

Second: Going into hiding isn't very proactive.

Third, if they are multinational then it would be "Governments" (plural) since they would have no one specific government.
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"When a multinational special ops team is set up by their superiors, they must..." (Then add what they -must do)
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Hope that helped, good luck with this!