Not a problem. First of all, the amount of any drug in 300mL of blood is going to be pretty low. The body has 42 liters of body water through which most drugs are dispersed evenly (not only the blood, but extracellular fluid in tissues) and then 7L of blood. So even if the dose was completely in the blood, 300mL will not contain more than 1/20 of the dose in the body, which is pretty negligible.
Also, for many surgeries patients are actually anti-coagulated, believe it or not. Especially in the case of surgery on the legs, there is risk of developing a thrombus while the patient is lying on the table for an extended time and the blood is more stagnant, so it is common to give heparin to anti-coagulate before many surgeries. Doctors always "err on the side of bleeding." If a patient develops a bleed, it is not a big deal, they give a transfusion and medically it is not a serious problem. However, clotting is much more difficult to reverse and exponentially more likely to be fatal. Disseminate intravascular coagulation is a very scary medical problem, and could lead to a heart attack or pulmonary embolism (clot in the lungs).