There are 2 types of blood thinners anticoagulants and antiplatelets. Simply:
Anticoagulants
Anticoagulants work by interrupting the process involved in the
formation of blood clots. They're sometimes called "blood-thinning"
medicines, although they don't actually make the blood thinner
NIH
Vitamin K is essential for those reactions. Warfarin (Coumadin) works
by decreasing the activity of vitamin K; lengthening the time it takes
for a clot to form.
Antiplatelets
Antiplatelet drugs, such as aspirin, prevent blood cells called
platelets from clumping together to form a clot.
A deeper understanding can be derived from looking up the individual medications: Clopidogrel (Antiplatelet) and Coumadin(Anticoagulant). I don't know which type your refering to, but they:
Anticoagulant and antiplatelet drugs work by stopping platelets from
adhering to one another and clotting proteins from binding together.
- Blood thinners can cause thrombocytopenia (low platelets). However, the platelets have to be severely low beneath 100,000 to cause spontaneous and uncontrollable bleeding that may cause death usually.
Many medications can cause low platelet count by causing immunologic
reaction against platelets, called drug-induced thrombocytopenia.
So basically on this stuff it takes you longer to clot and therefore increased the time you bleed.