Why 'cut' the old boot off? The new boot can't be cut on.....
The old boot should come off without too much trouble.
Clean, clean, clean, before installing the new boot.
Make sure the new boot slips under the little 'keeper tabs' on the swing arm.
Don't use oil to help slide the new boot on because it can make it rather difficult to hold the boot in just the right place while tightening the clamps. And oil will help the clamps slide off the boot when tightening.
Lord of the Bings, kangaroo farmer