No, he can be sacked by his own party but they are unwilling to do so. And he refuses to resign.
His government could be forced to resign if it were to lose a vote of no confidence, in which case, Jeremy Corbyn would be invited to form a new government. If Corbyn declines or his government itself faces a vote of no confidence and loses, as is likely, a general election must be called, which some say would give Boris a clear majority and lead to a No Deal Brexit.
Consequently, Jeremy Corbyn is refusing to call for a vote of no confidence until Brexit has been extended.
There are two alternatives, (a) Johnson calls for a vote of no confidence in his own government, or (b) the 'caretaker government'. Four of the six opposition parties plus 27 Tory rebels who have recently been thrown out of the Tory party would band together and agree to install Jeremy Corbyn as prime minister solely for the three weeks it would take to achieve a Brexit extension. But the Liberal Democrats aren't playing ball. Not just yet, anyway.
Corbyn is probably resigned to Boris Johnson's deal. However, there is much to play for in the next three months. It is likely that we will have a general election before Christmas and we cannot predict whether:
The Conservatives will win and consolidate Johnson's deal
There will be a hung parliament (my prediction) and a lot of wrangling
Labour will win (unlikely) and renegotiate the deal
The Liberal Democrats will win (extremely unlikely) and cancel Brexit
No party will win and the minor parties will negotiate a second referendum
To me, this says the fight could get very much more involved. Or it may be a flop.