Many herbs are thought to affect blood clotting. Most are suspected to decrease the effectiveness of the clotting process through many different mechanisms. This is an important issue to consider when combining certain herbs with medications.
Coumadin is the most well known blood thinner and has a very narrow therapeutic window. It is very difficult to get the dose just right and can be significantly affected by the use of herbs. I advise anyone taking Coumadin to be extremely careful when combining the use of vitamins and herbs with that medication as a miscalculation can be deadly.
Plavix is a little more forgiving. The biggest issue I can warn you about is combining multiple different anti-platelet herbs or vitamins with Plavix. For example, fish oil, vitamin E, CoQ10, Gingko biloba and garlic are all mildly thinning to the blood. If you are taking several of these in conjunction with the Turmeric and the Plavix you could be putting yourself in a dangerous situation. Also, if you are taking Plavix and aspirin together you should avoid the use of potentially blood thinning herbs.
Taking the Plavix and the Turmeric together does pose a theoretical chance, based on some studied information, that you will have an increased risk bleeding. Anti-platelet medication poses a unique risk when used in conjunction with certain herbs like Turmeric in the same way that you are now at a higher risk of a bleeding event by taking certain over the counter medications like aspirin, ibuprofen and even alcohol. I advise you to discuss your situation with your doctor before combining these two things.