The other answers do a good job of summarizing that yes, you can absolutely make an explosive collar with current technology. There are some edge case factors that might be relevant to consider.
If you have someone with the trigger who has some kind of moral issue with excessive collateral damage, wants to ensure that they definitely have the CORRECT target before the device goes boom, etc, then you might want to think about the use of an explosive cellphone on a terrorist leader by the Israeli Mossad in the early 2000s. The cell phone was used because the IDF could then confirm that the correct person was holding the phone. According to people who had knowledge of the operation, the main engineering challenge was NOT to make a fully functional cellphone with enough room in the case to house enough plastic explosive to blow someone's head off, but to keep the blast directed enough and small enough to ensure that there would not be collateral damage to other persons nearby. Israel didn't want to accidentally kill a waiter or something if the target was at a restaurant. An explosive collar would have a similar engineering consideration. It would only need a pretty weak explosion to take off someone's head if your charge were literally wrapped around their neck. In the case of the phone, I believe the back of the phone housing was reinforced with steel and shaped in a way to direct the blast out through the face of the phone. A collar would have a similar consideration, so the outside of the collar might be a steel housing that forces the blast from the charge inward.
Det cord was mentioned, but in my opinion, it would be overkill. We used to use that stuff to blow open steel doors... in my non-techie life... You probably would have a risk of collateral damage with normal sized det cord. Probably something about a quarter the diameter would be fine.
Waterproofing/weatherproofing is not a major problem. The explosives themselves can be waterproof. The major issue is to waterproof the battery container and make sure it doesn't accidentally short under certain environmental conditions. This is somewhat expensive (compared to cheap consumer electronics) but is a challenge that has absolutely been solved elsewhere.
There are ways to harness the natural electrical current of the human body. If you wanted to get fancy, you could possibly harness this to recharge a very small battery in the collar. This might not withstand rugged use/real life/weather etc however.
As far as detonation, the obvious choice is a cell-phone type trigger. This is used by lots of terrorists all over the world. It may be a bit risky to go this route though, since there are ways to send out a lot of signals that will preemptively detonate such devices in a given area. A better solution might be a combination of a radio signal and software that verifies the identity of the signal sender via a pre-selected code. That way some stray signal doesn't accidentally blow off your guy's head before it is time.
Answer: Totally Doable
All in all, if you invest some money and have some good engineering skills available, you could absolutely make a collar that would last a very long time, survive normal life, and only go boom when you want it to.