Only way we know how to activate alarm clock is through Nightstand mode which has alarm clock and normal clock but to enter nightstand mode is that you need to do following:
- Put your apple watch on side
- Connect the charger and let if fully charge
- After it got fully charged it will automatically go in Nightstand mode
This also works with Apple Watch Series 2 and Apple Watch Series 1.
Here is a video about Apple Watch Nightstand mode: