The Wallabies have been in impressive form throughout the tournament and topped a tough Pool A by winning all four of their matches, including contests with co-hosts England and Wales.
However, head coach Cheika believes Scotland's physical style will provide an even bigger threat.
"Yes. 100 per cent (this is our biggest challenge yet). This will be the most difficult game we play and that's not disrespecting our other opponents at all because every match has been tough but this will be the toughest," he said.
"There's going to be a lot of pain, it's going to be physical and I want the players to enjoy that as well because that's when it's worth it."
Australia, two-time World Cup winners, are the favourites for the clash at Twickenham, but Cheika added: "It's pretty easy because we don't think we are complacent. Nobody was saying that about us however many months ago it was and things aren't any different now.
"We're acutely aware that this is really important for our own journey as a team.
"I've seen a lot of the Scottish players saying they can win - and they can, they can. It's the reality of sport and what we need to make sure is that our mindset is really clear on what we're prepared to do to get that victory."