User-generated content (UGC) live videos are often bothered by various distortions during capture procedures and thus exhibit diverse visual qualities. Such source videos are further compressed and transcoded by media server providers before being distributed to end-users. Because of the flourishing of UGC live videos, effective video quality assessment (VQA) tools are needed to monitor and perceptually optimize live streaming videos in the distributing process. Unfortunately, existing compressed UGC VQA databases are either small in scale or employ high-quality UGC videos as source videos, so VQA models developed on these databases have limited abilities to evaluate UGC live videos. In this paper, we address UGC Live VQA problems by constructing a first-of-a-kind subjective UGC Live VQA database and developing an effective evaluation tool. Concretely, 418 source UGC videos are collected in real live streaming scenarios and 3,762 compressed ones at different bit rates are generated for the subsequent subjective VQA experiments. Based on the built database, we develop a Multi-Dimensional VQA (MD-VQA) evaluator to measure the visual quality of UGC live videos from semantic, distortion, and motion aspects respectively. Extensive experimental results show that MD-VQA achieves state-of-the-art performance on both our UGC Live VQA database and existing compressed UGC VQA databases.