Many robot demonstration datasets contain heterogeneous demonstrations of varying quality. This heterogeneity may benefit policy pre-training, but can hinder robot performance when used with a final imitation learning objective. In particular, some strategies in the data may be less reliable than others or may be underrepresented in the data, leading to poor performance when such strategies are sampled at test time. Moreover, such unreliable or underrepresented strategies can be difficult even for people to discern, and sifting through demonstration datasets is time-consuming and costly. On the other hand, policy performance when trained on such demonstrations can reflect the reliability of different strategies. We thus propose for robots to self-curate based on online robot experience (Demo-SCORE). More specifically, we train and cross-validate a classifier to discern successful policy roll-outs from unsuccessful ones and use the classifier to filter heterogeneous demonstration datasets. Our experiments in simulation and the real world show that Demo-SCORE can effectively identify suboptimal demonstrations without manual curation. Notably, Demo-SCORE achieves over 15-35% higher absolute success rate in the resulting policy compared to the base policy trained with all original demonstrations.