The pressurized liquid extraction (PLE) technique was used to obtain protein extracts with antioxidant capacity from salmon muscle remains, heads, viscera, skin, and tailfins. A protein recovery percentage ≈28% was obtained for all samples except for viscera, which was ≈92%. These values represented an increase of 1.5–4.8-fold compared to stirring extraction (control). Different SDS-PAGE profiles in control and PLE extracts revealed that extraction conditions affected the protein molecular weight distribution of the obtained extracts. Both TEAC (Trolox equivalent antioxidant capacity) and ORAC (oxygen radical antioxidant capacity) assays showed an outstanding antioxidant activity for viscera PLE extract. Through liquid chromatography coupled with electrospray ionization triple time-of-flight (nanoESI qQTOF) mass spectrometry, 137 and 67 peptides were identified in control and PLE extracts from salmon viscera, respectively None of these peptides was found among the antioxidant peptides inputted in the BIOPEP-UMP database. However, bioinformatics analysis showed several antioxidant small peptides encrypted in amino acid sequences of viscera extracts, especially GPP (glycine-proline-proline) and GAA (glycine-alanine-alanine) for PLE extracts. Further research on the relationship between antioxidant activity and specific peptides from salmon viscera PLE extracts is required. In addition, the salmon side streams studied presented non-toxic levels of As, Hg, Cd, and Pb, as well as the absence of mycotoxins or related metabolites. Overall, these results confirm the feasible use of farmed salmon processing side streams as alternative sources of protein and bioactive compounds for human consumption.