Aspirin indeed often has a blood-thinning effect. As such it may help reduce the risk of blood clots. That's the best case scenario, and even then it merely treats the symptoms, not the root cause of blood clots.

Blood clots and cerebral hemorrhage are the two sides of the coin. By popping an aspirin you shift the odds from blood clots to hemorrhage.

If I had to choose one of them, I'd take the blood clot.