Can over stimulation of saliva cause blood in saliva?

No: It is not normal to have blood in your saliva regardless of the amount of saliva produced. You most likely have some form of periodontal (gum) disease. See a dentist for a complete and thorough dental examination and periodontal evaluation.

No : Typically not. Blood in saliva can result from oral trauma (cheek biting, puncture / laceration of the soft tissues by a sharp piece of a nacho chip etc. It can also result from gum disease where the gums are so infected and spontaneously bleed. Best to be seen by a dentist to determine the cause and treat appropriately. All the best. Good luck.