Asprin is not given in a patient who is already on heparin because aspirin causes:
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
Platelet dysfunction
Aspirin inhibits the action of heparin
Enhanced hypersensitivity of heparin
Therapy of heparin cannot be monitored
Hematology