Asprin is not given in a patient who is already on heparin because aspirin causes:
Platelet dysfunction
Aspirin inhibits the action of heparin
Enhanced hypersensitivity of heparin
Therapy of heparin cannot be monitored
Aspirin inactivates cyclo-oxygenase by irreversible acetylation of the enzyme and thereby inhibit the synthesis of thromboxane A2. Thromboxane A2 normally promotes platelet aggregation. This COX inhibition lasts for 7 - 10 days till fresh platelets are formed. From medical pharmacology padmaja 4th edition Page no 344
Hematology