Yes, any opiod will lower your heart rate as well as your breathing, which may become more labored and much more shallow. Generally, your breathing will become too shallow and you will die from lack of oxygen before your heart rate becomes too slow from an opiod (oxycodone - the main active ingredient in oxycontin) overdose. However, you should be concerned if your heart rate falls below 60 bpm, as this has been known to cause heart failure in normal healthy adults. Unless you are an athlete and normally have a very low heart rate, you should seek a medical doctor's advice or call 911 if you believe your heart rate drops below 60 beats per minute to be safe.
Good luck and have fun, but stay safe. Opiates can be a great experience but they are not worth risking your life.
Sources:
wikipedia, webmd, 3 years of heroin addiction