You cannot delete HMs in Yellow. It is said in the game that HM moves are permanent. If you will need to use HM's such as flash and cut that are not too useful in battles, just teach it to Pokemons that you will not use in battles so that your main roster's skills will be strong moves.
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To delete an HM move, you must go to the move deleter in Fushia city. He can delete any move you want to... even a HM move! but don't forget that after that HM is deleted that Pokemon only has 3 moves left so teach it another move!
the move deleter in canalave city :) =)
There is no move deleter in Pokemon Blue - however, there are Gameboy Genie and GameShark codes to aid in the removal of HM moves from the early games.
The only way to delete HM's is to have the Move Deleter in Canalave City do it for you.
In Fuchsia City, the Move Deleter lives in the house on the left of the Pokemon Center. He can make your Pokemon forget moves, including HM's.Go to fuschia city and head to the Pokemon center but enter the house right to the left of it inside is a guy who calls himself the move deleter choose the Pokemon you want to delete the HM move from choose the HM move and say YES to get rid of it.