Target-oriented opinion summarization is to profile a target by extracting user opinions from multiple related documents. Instead of simply mining opinion ratings on a target (e.g., a restaurant) or on multiple aspects (e.g., food, service) of a target, it is desirable to go deeper, to mine opinion on fine-grained sub-aspects (e.g., fish). However, it is expensive to obtain high-quality annotations at such fine-grained scale. This leads to our proposal of a new framework, FineSum, which advances the frontier of opinion analysis in three aspects: (1) minimal supervision, where no document-summary pairs are provided, only aspect names and a few aspect/sentiment keywords are available; (2) fine-grained opinion analysis, where sentiment analysis drills down to a specific subject or characteristic within each general aspect; and (3) phrase-based summarization, where short phrases are taken as basic units for summarization, and semantically coherent phrases are gathered to improve the consistency and comprehensiveness of summary. Given a large corpus with no annotation, FineSum first automatically identifies potential spans of opinion phrases, and further reduces the noise in identification results using aspect and sentiment classifiers. It then constructs multiple fine-grained opinion clusters under each aspect and sentiment. Each cluster expresses uniform opinions towards certain sub-aspects (e.g., "fish" in "food" aspect) or characteristics (e.g., "Mexican" in "food" aspect). To accomplish this, we train a spherical word embedding space to explicitly represent different aspects and sentiments. We then distill the knowledge from embedding to a contextualized phrase classifier, and perform clustering using the contextualized opinion-aware phrase embedding. Both automatic evaluations on the benchmark and quantitative human evaluation validate the effectiveness of our approach.