How long does it take for the clotting effects to wear off. Assuming one dose of around 600mg of aspirin and exactly how much effect does it have on clotting of minor bleeds?
According to Tulane's pharmwiki, the half-life of aspirin for a dose of 300-650 mg is 3.1-3.2 hours. The half life of a drug is the amount of time needed for the concentration of drug to be reduced in half (after reaching peak concentration).
So, after 5 half-lives, or roughly 16 hours, the amount of drug remaining in the body is (1/2)^5 = 0.03125 -> 3%, which is mostly eliminated from the body.
*I only use 5 half-lives because it was a rule of thumb for drug elimintion mentioned in the Youtube video in my references. A more conservative answer could be 6 half-lives (1.5625% drug remaining in blood) or rougly 19 hours.
Aspirin functions as a blood thinner by irreversibly inactivating a protein called the COX enzyme in platelets, which disrupts the clotting process. This is why a possible serious side effect of taking aspirin is bleeding a lot from a minor cut.
In summary, in those 16 hours in which the aspirin is in action, the platelets (life span: 8-9 days) that are affected will be unable to clump together to clot which can pose a risk for minor bleeds.