Enzymatic hydrolysis-offline and membrane separation (EH-offline MS), enzymatic membrane reactor (EMR) (various operational modes), and conjoined nanofilter-purification (desalination) were used to produce highly stable antihypertensive and antioxidative peptides from ultrasonic-slurry viscosity reduced sea cucumber (A. japonicus) protein. The adoption of the optimum batch parameters by EMR-gradient diafiltration feeding (GDF), water feeding, and substrate feeding ensured a significant (p < 0.05) enhancement in protein conversion degree (PCD) by 60.39, 46.69, and 23.33%, respectively, over the conventional EH-offline MS. Also, the antihypertensive activity (ACE-inhibitory potency) of the peptides produced was in the order EMR-GDF > substrate feeding > water feeding > batch process > EH-offline MS. The EMR-GDF and nanofilter-purification produced highly digestible peptides with ACE-inhibition activities of 79.44% and 77.57% for gastric and gastrointestinal digests, respectively. Peptides with molecular weights of 1000–500 Da and 500 Da significantly contributed to the antihypertensive potency of desalinated peptides. In vitro simulated peptides showed a significant increase in the hydroxyl radical scavenging activity for gastric (77.27%) and gastrointestinal (85.32%) digests. The antioxidative stability of the produced peptides was least affected by high-temperature storage. The high arginine (Arg) and hydrophobic amino acid (HAA) content of the peptides resulted in their improved digestibility. Therefore, conjoined EMR-GDF and nanofilter-purification in the production of highly stable desalinated bioactive peptides for industrial applications could be a viable alternative.