Once you've reached Ilex forest, there will be a boy who lost a farfetch'd. Go and try to force it back to the boy. Then the owner is there and he will reward you with HM02.
Edit: It's HM01, not HM02. HM02 is for Fly.
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How to get the hm cut in pokemon glaze
You can use the HM cut in Pokémon Gold to cut down trees that block the way. You can get cut in Ilex Forest.
only Pokemon with sharp claws can learn the hm cut
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. :)
you cant