Protesters interrupted a celebration of Chicago’s 175th birthday Sunday at which Mayor Rahm Emanuel spoke by blasting his budget plan to close six mental health clinics, contending the plan will make it harder for people to get help and cost lives.

“History will judge,” the small group shouted as Emanuel stood by a birthday cake with children and others gathered at the end of the Chicago History Museum celebration program Sunday.

The museum hosted a day-long program on the city’s founding, a children’s choir, a panel discussion on the city’s identity and with actors dressed as historical figures, including founder Jean Baptiste Pointe DuSable.

Emanuel spoke on the city’s history and future. “We have come to forks in the road . . . and yet we have never shrunk from our challenges,” Emanuel said. “And this is a story of the city and it’s a story still being written.”...