The Swans scored a stirring victory over West Coast in Perth last weekend, which lifted them into third spot on the ladder.
But Mumford says fronting up against his former club will be an even greater test.
"The Cats are a great side and it is going to be a massive test to see where we're at," Mumford said on Thursday.
"We'll have to play even better than we have been and see how we go."
The Swans have lost eight consecutive games against the Cats, although the teams haven't done battle at the SCG since Nick Davis' heroics booted the Swans into the 2005 preliminary final on their way to their first flag in 72 years.
"I know Geelong made their home ground a fortress and we're aiming to do the same thing with the SCG up here," Mumford said.
"We're hoping a big crowd will turn out and help us get over the line."
Geelong forward Steve Johnson shapes as a crucial player in the match but preparation for this week has been different at for Johnson and his fellow Cats with parts of Skilled Stadium roped off to try and replicate the conditions they'll face while running around on the AFL's smallest ground.
"We did a couple of drills yesterday, which were a bit shorter than usual," Johnson said.
"On different grounds you like to move the ball in different ways.
"Against Fremantle [at Patersons Stadium in round two] we probably tried to use the space a little bit more, but at the SCG, it's only two big kicks to get it deep into the forward line.
"We know there's going to be a lot of contested ball on Saturday night and our big focus will be getting numbers around the ball all the time."
