Prostaglandins are hormone-like substances in the body that either encourage or inhibit blood vessel expansion and contraction. They participate in both platelet creation and destruction. As a result, prostaglandins play a part in inflammation because they can encourage rubor (redness), swelling of the tumor, and pain (dolor).
Salicylate, a component of aspirin, a nonsteroidal anti-inflammatory medication (NSAID), reduces prostaglandin-induced inflammation in the body. The medicine directly interferes with the production of prostaglandins, which prevents the development of blood clots.
Reference: Britannica. (2023, Aug. 25). Aspirin. Science and Tech. https://www.britannica.com/science/aspirin
Simply, aspirin/salicylic acid inhibits the enzymes (Cyclooxygenase-1 (COX-1) and Cyclooxygenase-2 (COX-2). These enzymes are involved in the synthesis of Thromboxane A2 that is involved in amplification of platelets activation and platelets aggregation. Once these enzymes are inhibited, no synthesis of Thromboxane A2, therefore there is no platelets aggregation.