How does EDTA prevent blood samples from clotting? How does removing calcium from the sample keep it from clotting?
You have already included the answer in your question. :)
Blood clotting is a very complex process and it involves a number of factors: Calcium is considered as one of the most important clotting factor in the list-- i.e. number IV .
EDTA is ethylene-diamine-tetraacetic-acid. It is a colourless solid, used as anticoagulant of blood. EDTA can chelate not only calcium but a variety of divalent metal ions to form a stable ring like structure.
When calcium is removed from blood sample by adding EDTA in it, specific steps leading to blood clotting will not be completed: hence blood will not clot.