Blood clumping in mosquitos
Female mosquitoes need blood for laying their eggs. This actually means that they need a source of rich protein and iron for their kids and hence, prey on us. 
It is worthwhile for us to pause here and ponder over the difference between clumping and clotting before proceeding to the actual answer. 

Agglutination tests as you may have come across are essentially antigen antibody reactions visible to the naked eye. Antibodies and antigens (on the RBCs) bind leading to the clumping that you talk of.
Clotting on the other hand is a complex set of reactions involving the thrombins and the platelets.

When a person is transfused of a wrong blood type, as in blood of another group is injected into his blood, something very bad is ought to happen. The clumping is extensive (an immune reaction) which leads to a clotting reaction, leading to a condition called DIC (Disseminated Intravascular Coagulation). This is an emergency situation since there can even be Acute Kidney failure.

Coming to the mosquito,


In the human case, we injected into the blood. Here it gets into the gut. The gut has enzymes which breaks down the proteins. Theres no antibody no antigen left out there!! Proteolytic enzymes start right from the very beginning. 
Even if some clumping occurs, it doesn't actually matter. It mattered in the human case since it was a transfusion and the sequelae mattered. 
Another important thing to keep in mind is we are talking only of clumping and not clotting. The mosquito takes care of clotting by secreting anticoagulants into the blood stream right when it is ready to have it meal. Clumping on the other hand, per se, doesn't turn the blood into a clot. If you have seen blood clumping in agglutination test, its not such a dramatic thing to occur. The blood still stays in liquidy. So clumping wouldn't pose much of a problem.


Hope this helps! Sorry but the climax wasn't that dramatic :)