Yes. You can also get it deleted by a guy in Johto in Blackthorn city. If you want the HM back later again you can teach it to the Pokemon again.
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You can get more than one starter Pokemon by trading with another person.
You have to beat the first gym and then you'll get the HM cut. Just teach the HM cut to one of your pokemon. :)
Inside Drayden's house, Iris will teach you Draco Meteor. In white, Drayden will teach you because you will be fighting iris in the gym.
No one in the game will do that for you.
You can get more than one by matching all of the digits in the lottery.