When you are in the town with the first Gym, go to the Sprout Tower. Battle your way to the top to fight the Buddhist Grandmaster guy; he'll give you Cut once you beat him. Happy gaming. EDIT: Opps sorry; yeah Timmy1991 is right (Comment below); Sprout Tower is HM Flash. Sorry; I'm used to Cut being the first HM so the first place where you get HM in HG/SS came to mind; Sorry once again ><' But anyway; For the Farfetch'd hunt, make sure you sneak up behind them. Also; Thanks for the correction Timmy1991
Sorry but no.... You have to go to Azalea Town talk to Kurt (the pokeball maker), Follow him to the well just east of town, fight team rocket, return to the town, beat Bugsy, go to the western entrance of the town, beat your rival, go into Ilex forest, talk to the guy in the forest, find both of his Farfetch'd, and he will then give you Cut....
No, they'll be out in Spring 2010. There's a fan translation though. https://www.romulation.org/forum/index.php?topic=23083.0 Try not to hijack threads in the future.
@Daowiies Chasing the Farfetch'd is doing me no good. Going behind them isn't working, because I just fail like that. Could you please further explain this?