The anti-coagulation action is one that cuts of difficult that process at some of its stages. Let's see if telling you quite simply the coagulation process will let you undestand the anti-coagulation one. When a blood vessel is broken, blood escapes as long as the flesh wound still is open, and the pressure within the vessel exceeds the outside one. Pressure can be equalized by different factors. Anyway usually shed blood clots quickly.
Coagulation is a change that is studied by many scientists with different theories.
The clotting of blood is due to the sudden appearance of fibres that entangle the blood cells. During the very complex process, it occours the formation of a polymerized protein called fibrin from another protein, the fibrinogen. Fibrinogen is produced by the liver and is converted to fibrin by the way of thrombin. Thrombin does not exist in the normal circulation but is generated from a precursor, the prothrombin. Now prothrombin is a rather stable protein formed in the liver by a process requiring vitamin K, and any deficiency of this vitamin depress the production of prothrombin and also of other clotting factors.