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1.
A gentle challenge or rejoinder to a fanciful or bullshit statement or a tall tale. An idiom you use to tell someone that you do not believe what they have just said.

Derived from the game where you ask someone to "pull my finger" and fart, then ask them to "pull my other finger" or "now pull the other one".
-- Example 1 --

GUY 1:
"Yeah I drank about 20 beers but the cop couldn't tell I was drunk and let me go."
GUY 2:
"Pull the other one. I don't think so."

-- Example 2 --

From Scene 1 of Monty Python and the Holy Grail:
KING ARTHUR:
Whoa there!
clop clop clop
SOLDIER #1:
Halt! Who goes there?
ARTHUR:
It is I, Arthur, son of Uther Pendragon, from the castle of Camelot. King of the Britons, defeater of the Saxons, Sovereign of all England!
SOLDIER #1:
Pull the other one!
ARTHUR:
I am,... and this is my trusty servant Patsy. We have ridden the length and breadth of the land in search of knights who will join me in my court at Camelot.
I must speak with your lord and master.
SOLDIER #1:
What? Ridden on a horse?
ARTHUR:
Yes!
SOLDIER #1:
You're using coconuts!
ARTHUR:
What?

by Warren Fwy August 15, 2006
 
2.
Sarcastic response to someone who is taking the mickey

Shortened version of "Pull the other one, it's got bells on it."
"A truthful politician? Pull the other one!"
by nzowl December 15, 2003