Graduate-student workers at Yale University staged a large demonstration Monday just before the school’s commencement ceremony, their latest attempt to draw attention to their unionization push.

Thousands of people marched through downtown New Haven, Conn., wearing orange T-shirts and mortarboards, carrying balloons and holding signs that read, “Just the beginning, Yale.” The group, which included graduate students and labor activists, jeered school administrators as they began the commencement procession onto the campus,...