Remove the old or broken part by pulling it off if it's loose enough.

I made sure to keep the bite valve and the part of the hose around it submerged in the boiling water.

Ensure the end of the hose is cut at a 90-degree angle to avoid cutting yourself. Make sure your hand is far from the scissors while keeping a stable grip.

Once you're certain that nothing else is in the way of the scissors, make the cut.