HM Moves
In "Pokemon Silver" there are seven HM moves: Cut, Fly, Surf, Strength, Flash, Whirlpool and Waterfall. When you choose to teach one of these moves to a Pokemon you will see a message explaining that once they have been taught they cannot be removed. Therefore, carefully consider which Pokemon you teach the HM moves. You will eventually be able to delete HM moves, but not until much later in the game.
Learning New Moves
When your Pokemon levels up, it learns new moves. In "Pokemon Silver," when a Pokemon wants to learn a new move, you are given the option to forget an existing move and replace it with the new move. When given this option, any HMs that your Pokemon has learned will not be available to be forgotten.
Move Deleter
If you visit Blackthorn City in a house at the south end of the town, you will find a man called the Move Deleter. He will let you delete any of your Pokemon's moves, including HMs. This will free up space for your Pokemon to learn a new move instead of the HM. This is the only way to remove HM moves in the game.
Action Replay
You can remove HMs in the game by using an action replay code. Enter the following code into the Action Replay then press "Select" and "Up" in game to activate the code:
94000130 ffbb0000
62111880 00000000
b2111880 00000000
d5000000 00000000
c0000000 00000063
d6000000 000009b0
d2000000 00000000
This removes all HMs from the game, including the ones your Pokemon have learned.