WASHINGTON—President-elect Donald Trump vowed anew on Friday to dismantle the 2010 Dodd-Frank financial overhaul, at the same time his transition team is tempering expectations for a full repeal of the sweeping law, people familiar with the matter said.

Instead, Mr. Trump’s team is focused on rescinding or scaling back the individual provisions Republicans find most objectionable, such as the Financial Stability Oversight Council’s authority to designate large nonbanks systemically important and thus subject to tougher regulation...