Lay the paper towel roll on a sturdy flat surface. Use one hand to hold the roll still and the other hand to cut the roll in half. A serrated or electric knife are the best tools. Watch those fingers!
Use the same serrated or electric knife to cut the cardboard insert out. Go along underneath the cardboard insert with the knife.
Create a back and forth motion with the knife as you go underneath the cardboard insert. You will be making a stabbing motion that swings to the right and left as you press forward underneath the insert. This will create some dust and will damage some of your wipes, but it can be done.
Remove the cardboard insert once you've slid the knife underneath the cardboard, loosening it from the paper towels. You may need to go back and slide the knife under again if the insert doesn't break clean away from the paper towels.
Repeat this process on the other half of the paper towels roll. Remove the damaged paper towels from the stacks. You now have two sets of paper towels ready to be made into wipes.