Protease that catalyzes two essential functions in the SUMO pathway (PubMed:11896061, PubMed:12192048, PubMed:15296745, PubMed:20194620, PubMed:21965678). The first is the hydrolysis of an alpha-linked peptide bond at the C-terminal end of the small ubiquitin- like modifier (SUMO) propeptides, SUMO1, SUMO2 and SUMO3 leading to the mature form of the proteins (PubMed:15296745). The second is the deconjugation of SUMO1, SUMO2 and SUMO3 from targeted proteins, by cleaving an epsilon-linked peptide bond between the C-terminal glycine of the mature SUMO and the lysine epsilon-amino group of the target protein (PubMed:15296745, PubMed:20194620, PubMed:21965678). May down- regulate CTNNB1 levels and thereby modulate the Wnt pathway (By similarity). Deconjugates SUMO2 from MTA1 (PubMed:21965678). Plays a dynamic role in adipogenesis by desumoylating and promoting the stabilization of CEBPB (PubMed:20194620). Acts as a regulator of the cGAS-STING pathway by catalyzing desumoylation of CGAS and STING1 during the late phase of viral infection (By similarity). {ECO:0000250|UniProtKB:Q91ZX6, ECO:0000269|PubMed:11896061, ECO:0000269|PubMed:12192048, ECO:0000269|PubMed:15296745, ECO:0000269|PubMed:20194620, ECO:0000269|PubMed:21965678}. This is the function of SENP2 (SUMO specific peptidase 2, Ensembl gene identifier ENSG00000163904).