The only way to delete HM's is to have the Move Deleter in Canalave City do it for you.
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Canalave City, go to the house above the Pokemart & yes, he does delete HM moves!
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!
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.
the move deleter in canalave city :) =)
Move deleter. Canalave City.