How do you get cut in sapphire?

Next to the Pokemon center in rustboro city, there is a man's house, go inside talk to the man and he will give you cut.

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Beat Roxanne in Rustboro City, then go to Cutter's house and speak to the man, and he will give you HM01 - Cut

In the house next to the Pokemon center in Rustboro City.

Cut (HM01) can be found in Rustboro City