Considering the global increase in fish consumption, the growing side-streams coming from the fish supply chain (e.g., skin, fins, tail, heads…), also including undersized or “unwanted catches”, have been recently proposed as source of high-value bioactive compounds (e.g., peptides and fatty acids). In this case study, hydrolyzed collagen peptides (HCPs) were extracted from different parts of Mugil cephalus L. using environmentally friendly techniques such as ultrasounds and enzymatic treatments. Both a mixed biomass derived from the skin, fins, and tail, and a whole fish, were considered as starting biomass, simulating the unsorted processing side-streams and an undersized/unwanted catch, respectively. The extracted HCPs were purified in fractions (<3 KDa and >3 KDa) whose yields (about 5% and 0.04–0.3%, respectively) demonstrated the efficiency of the hydrolysis process. The extraction protocol proposed allowed us to also isolate the intermediate products, namely the lipids (about 8–10%) and the non-collagenous proteins (NCs, 16–23%), whose exploitation could be considered. Each sample was characterized using Sircol, UltraViolet-Spectra, and hydroxyproline assay, and the viability of their collagen fractions was tested on human endothelial cells. Significant effects were obtained at a fraction of <3 KDa, in particular at a concentration of 0.13 µg/mL. The T-scratch test was also performed, with positive results in all fractions tested.