Yes there is a way to get Mew in Pokemon Red Blue and Yellow but not fire-red or Leaf Green. Mew can Be traded into Pokemon Gold,Silver,Crystal and then can be copied using a glitch.

Don't Fight this Gambler

Or this guy

Save your game at the underground path.
Saving after this will mess up the glitch

Take one step and press start

Fly or Teleport to Cerulean City

Fight this guy let him walk to you otherwise your will have to do the glitch again

Fly to Lavender Town go on Route 8(See Photo) Your Start Menu will pop up press B to close it and