Is it possible for you to refuse doctor's blood testing?

Yes: You have a right to refuse treatment, period, unless you are a threat to public health or you have just injured yourself in an attempt to harm yourself. At least this is the law in the usa. However, it's best if you talk about your reasons with your physician -- unless you have a good reason to want to become / stay sick (i can't think of any), bloodwork is hugely helpful.