Avocado seed and peel are the main by-products from avocado industrialisation, and account for nearly 30% of fruit weight. Although they are usually discarded, their high phenolic content has been deeply associated with several nutritional and functional benefits. Thus, for a comprehensive analytical evaluation of both semi-industrial extracts, various steps have been developed: tentative characterisation and quantification of the phenolic composition using HPLC-ESI-qTOF-MS, determination of TPC and antioxidant activity by Folin–Ciocalteu, FRAP, TEAC and ORAC methods, evaluation of scavenging capacity against different ROS and measurement of the enzymatic inhibitory potential against potentially harmful enzymes. Finally, their bioactive potential was tested in a human platelet model where antiaggregatory activity was measured. Hence, 48 different compounds were identified, where flavonoids and procyanidins were the most representative groups. The higher TPC was found in avocado peel extract (190 ± 3 mg/g), which showed more antioxidant power and more capacity to decrease ROS generation than seed extract (60 ± 2 mg/g). In addition, both extracts showed enzymatic inhibition, especially against hyaluronidase, xanthine oxidase and acetylcholinesterase. Lastly, avocado peel was proven to inhibit platelet aggregation with significant results at 1, 0.75 and 0.5 mg/mL, where the extract showed reducing effects on agonists’ expression such as p-selectin or GPIIb/IIIa complex. These results demonstrate that both semi-industrial extracts—above all, avocado peel—have an interesting potential to be exploited as a natural by-product with antioxidant properties with multiple applications for the prevention of different pathologies.