His former New Democrat MP defected to the Ontario Liberals last month and is now running in a provincial byelection.
Mulcair said he still doesn't fully understand why Thibeault quit his party so suddenly.
"People are sad, but they're not angry. But they do want the people of Sudbury to know who they're dealing with,” he said.
“I mean, if this guy can just up and walk away and dump everything there, he can do the same thing again."
Mulcair will take part in a rally for provincial NDP candidate Suzanne Shawbonquit tonight in Sudbury.
There is also a federal election on the horizon. Despite defections of MPs like Thibeault, Mulcair said he feels his party has never been in a better place.