In Pokémon FireRed and LeafGreen, HM01 Cut is obtained by talking to the Captain on the top floor of the S.S. Anne in Vermillion City.
To get to Vermillion City and board the S.S. Anne, you must first help out Bill in his house north of Cerulean City.
And then to actually use Cut, the Cascade Badge is required, which you’ll earn from Misty after defeating the Cerulean City Gym.
Before you can head to the S.S. Anne and get your HM, you need to help Bill.
If you don’t help Bill, you won’t even be able to make it to Vermilion City because a cop will stop you from entering the building you need to walk through.
How To Help Bill & Get The S.S. Anne Ticket
In order to find and help Bill, you need to:
Step 1: Head north of Cerulean, defeat your Rival, and cross the yellow bridge.
Step 2: Take a right after the bridge. This leads you onto Route 25.
Step 3: Continue right until you reach Bill’s house.
Step 4: Talk to the Pokémon in the house and then use the computer.
Step 5: Defeating Misty in the Cerulean City gym. This step is optional for getting the HM, but it is necessary if you actually want to use HM01.
You can technically get Cut first and then return to Cerulean to defeat Misty, but you will not be able to cut down any trees until you have the Cascade Badge.
Getting From Cerulean City To Vermilion City
Once you help out Bill, the Cop that was standing in front of the building we need will move to the side and allow you to enter.
Now that we can enter the building, we can make our way to Vermilion City, board the S.S. Anne, and get HM01.
Head to the building on the right side of Cerulean City with the cop standing out front. Enter the building and walk through the hole in the back wall.
After you exit the back of the building, take the path south, which will lead you under Cerulean.
Keep heading south until you reach a tiny building with a sign out front. This is the Underground Path that leads from Cerulean City to Vermilion City.
Simply enter the Underground Path building, head down the stairs, and walk through the tunnel until you reach the next set of stairs that will take you to the surface.
After you exit the Underground Path, head south and you’ll reach Vermilion City.
Boarding The S.S. Anne
Once you’re in Vermilion City, head south and follow the Dock below the city.
At the end of this dock, there will be a Sailor blocking your path before you can board the ship.
If you have the S.S. Ticket (which you do), you’ll flash it and the Sailor will allow you to board. Once you can board, just walk into the Ship and you’ll enter the S.S. Anne.
Make Your Way To The Captain
Step 1: Head left on the first floor and take the stairs up.
Step 2: On the second floor head down and then to the right. Then walk north towards the stairs in the corner.
Step 3: Defeat your Rival and walk up the stairs.
Once you’re in the Captain’s room, walk up to him and press A to interact with him. This will make you rub the Captain’s back as he gets sick.
To reward you for your hard work and empathy, the Captain will give you HM01 Cut, which you can then teach to your Pokémon!