With the rise of online learning, many novice tutors lack experience engaging students remotely. We introduce TutorUp, a Large Language Model (LLM)-based system that enables novice tutors to practice engagement strategies with simulated students through scenario-based training. Based on a formative study involving two surveys (N1=86, N2=102) on student engagement challenges, we summarize scenarios that mimic real teaching situations. To enhance immersion and realism, we employ a prompting strategy that simulates dynamic online learning dialogues. TutorUp provides immediate and asynchronous feedback by referencing tutor-students online session dialogues and evidence-based teaching strategies from learning science literature. In a within-subject evaluation (N=16), participants rated TutorUp significantly higher than a baseline system without simulation capabilities regarding effectiveness and usability. Our findings suggest that TutorUp provides novice tutors with more effective training to learn and apply teaching strategies to address online student engagement challenges.