What Causes Bleeding From Mouth?

I am 56 year old man. I have diabetes, and had undergone open heart by-pass surgery one and a half years back. After the surgery, my diabetes is under control and everything is normal.But, since a month, I am experiencing bleeding from the mouth. The colour of the blood is kind of Black. This happens only in the morning when I wake up. I used to take Aspirin and Plavix.A cardiologist told me to stop taking Plavix. But even after this, the bleeding continues.Is this a serious problem? If yes, what is to be done?