Catalyzes the transfer of sulfur from 3-mercaptopyruvate to a thiol-containing acceptor to form an intramolecular disulfide releasing hydrogen sulfide and pyruvate. 2-oxo-3-sulfanylpropanoate + [thioredoxin]-dithiol = [thioredoxin]-disulfide + H(+) + hydrogen sulfide + pyruvate The N-terminal region is the non-catalytic domain; the C-terminus contains the active-site cysteine residue and the CGSGVTA motif probably responsible for substrate specificity. Contains two rhodanese domains with different primary structures but with near identical secondary structure conformations suggesting a common evolutionary origin. Only the C-terminal rhodanese domain contains the catalytic cysteine residue (By similarity).