Can you take ashwagandha when you are diagnosed with supraventricular tachycardia and are on metoprolol tartrate??

No. I would not take any supplements at all that you don't first clear with a cardiologist. Heart rate issues can be affected by many supplements.

If the diagnosis of supraventricular tachycardia was made by your physician based on ECG documentation, I would ask that question of the physician who made the diagnosis. I am not aware of any effects, beneficial or harmful, from Ashwagandha. I do know that supraventricular tachycardia can recur and can be easily treated by a cardiologist/electrophysiologist. I wish you luck.