Parsing sentences to linguistically-expressive semantic representations is a key goal of Natural Language Processing. Yet statistical parsing has focused almost exclusively on bilexical dependencies or domain-specific logical forms. We propose a neural encoder-decoder transition-based parser which is the first full-coverage semantic graph parser for Minimal Recursion Semantics (MRS). The model architecture uses stack-based embedding features, predicting graphs jointly with unlexicalized predicates and their token alignments. Our parser is more accurate than attention-based baselines on MRS, and on an additional Abstract Meaning Representation (AMR) benchmark, and GPU batch processing makes it an order of magnitude faster than a high-precision grammar-based parser. Further, the 86.69% Smatch score of our MRS parser is higher than the upper-bound on AMR parsing, making MRS an attractive choice as a semantic representation.