Potassium does't "slow down the heart" unless the level is very high. The gradient (difference) between intracellular K+ (high number) and extracellular K+ (low number) influences the cell membrane's ability to depolarize. A big gradient (low K+) makes the membrane depolarize more easily. Depolarization leads to contraction.
We care about this because cardiac cells have the unique ability to 1) depolarize on their own, without a nerve to goose them into action (unlike, say, skeletal muscle, that will just lie there unless a nerve tells it to do something), and 2) spread their depolarizing cell-to-cell to all their neighbors (also unlike, say, skeletal muscle). What this means is that if a cell wall is already a little cranky from hypoxia or anything else and the serum K+ around it is low, it can depolarize whenever the heck it feels like, spreading a wave of depolarization throughout the ventricle. Because this happens outside of the control usually exerted by the cardiac conduction system, it results in funny-looking premature tracings on the EKG, called "PVCs," premature ventricular contractions.
We care about THAT because if a depolarization wave hits a cell in a particular phase of its repolarization, the result can be a chaotic rapid heartbeat that pumps no blood. This is why we watch K+ levels particularly in anyone with any sort of cardiac crankiness or reason to have cardiac crankiness, like MI, ischemia, or surgery.
Digoxin and slows the heart rate (from the SA node) and increases contractility in a failing heart by affecting calcium in the cells (and it does that by affecting the sodium pump in the cell membrane), and decreases AV conduction, a good idea in atrial fibrillation when you don't want to whip the ventricles into a frenzy (a lot of AF folks have ventricles that won't like going too fast).