There are MANY natural substances (herbs, supplements) that can help thin the blood and stop it from clumping. I would hop over to Tony Isaaic, Natural Healing and Iodine for some help.
Off the top of my head,
cayenne pepper * I know it stops bleeding, but I still think this one would help too, run it by uniy, tony or luella to be sure
enzymes like wobenzyme and serreptase help break down fibrogens, so it should work on clots too, blow this one by Uniy (Natural Healing), Tony, Luella and et.al on the Iodine supplementation
Iodine - helpful in breaking up fibroids, cysts and kicking out harmful fluoride, bromide, mercury, arsenic... AND, keeps our boobs soft and healthy, our female plumbing happy and our thyroid healthy...
Of course, the key to this is finding out the underlying issue that causes your problem in the first case, rather than treating the symptoms like alopathic docs do. Ya figure that one out and you're golden...