Does clonidine 0.1 mg., as a blood pressure prescription, have the effect of slightly slowing the heart beat/rate? Is it a beta blocker?

Yes...and No. Clonidine's central nervous system effects reduce the release of stress substances thereby lowering BP and mildly slowing ones heart rate. There a re two potential mechanisms for these effects, one of which is alpha2 receptor stimulation. It is not a beta blocker.
It's not. Clonidine is a centrally acting alpha-2 stimulator (what we call an agonist). It works on the feedback loop for adrenaline responsive nerves, and rather effectively. ~4% of people will experience bradycardia with it.

Related Questions

What is the lowest heart beat rate that could be considered normal? Also please tell me what the lowest normal diastolic blood pressure is.

Heart rate. Heart rate can be very variable patient to patient an athlete can have a resting hr of 30-40 and that would be normal . It really depends if you are dizzy of lightheaded . Below 40 in most ppl is a bit too low. Read more...