WASHINGTON—Another round of staff changes buffeted President-elect Donald Trump’s transition team Tuesday amid resistance from within the Republican Party over a top choice for secretary of state.

Vice President-elect Mike Pence formally signed documents that put him in charge of the transition team, and officials insisted the 10-week effort to build an administration is on schedule. In one of his first moves, Mr. Pence ordered the removal of all lobbyists from the transition team, said one transition team member with knowledge...