I take a beta blocker for hypertension. after pushmowing my yard, my bp is 103/60 and my heart rate is 97. is this ok?

Yes: Beta blocker, specially selective beta-1 blocker are often used in conjunction with other antihypertensive medication to treat for hypertension. Normal heart rate range from 60 to 100 BPM. Minimal cardiac perfusion pressure is mean arterial pressure > 60-65 mmHg or diastolic pressure + 1/3 (systolic pressure - diastolic pressure). Consult your doctor if your hear rate is < 60 BPM or dizziness.

Dose vs heart: Your blood pressure is too low for the kind of exercise you did and does not correspond to the rapid heart rate. I would suspect the possibility of actual damage to your heart and you should obtain immediate attention. Your dose of beta blocker if excessive should lower your heart rate too, and without that, question of heart damage is raised.

Yes: yes it is OK your heart rate is high for patient at rest but your medication had protected your heart after strenuous activity and kept it below hundred your BP is within normal limit

Yes: Normally during exercise or strain, BP and HR goes up. But you are on beta blocker so this seems to be OK.