How Do You Clean The Cage When There Is Newborn Hamsters In There?

Usually you can't change the cage until a certain time passes. The mother hamster will be very stressed out(seeing hands trying to pick up its babies) and might bite.Sometimes it will even eat its own babies.......
I hope this helps!

Either VERY CAREFULLY lift them out one by one buy just scooping them up, or wait for a few months (1-2 months) until they get older and scoop them out, unless you are literally GAGGING when you walk by the cage, then you should just try scooping them out, to scoop out try putting your hands UNDER the begging that is under the baby hamsters and just lift them up with the bedding.

Dude you can not touch does babies, well mostly you can use a spoon and pick up the babies well that would be tricky because the mother is very mad when you do that and don't use your hands the scent shall change and the mother will be mistaken because she ate her own babies. So you should leave them for two weeks and and that's the right time for them and you could touch the babies for a brief period.