I am unsure if the caterpillar can make more than one cocoon but it offers an opportunity for an interesting experiment! You could use this as an opportunity to introduce the scientific method to your child.

First, we ask a question: If caterpillars fail to make a cocoon, or loose their silk in some way, can they create another cocoon?

Then we can collect information to inform a hypothesis: For example, we know that caterpillars have to eat a certain amount before creating a cocoon (there are some arctic caterpillars that take 7 years to make a cocoon!). Maybe if the silk is removed the caterpillar will just continue to eat until it has enough nutrients to make more silk.

Then we make a hypothesis: The caterpillar will continue to eat and then make another cocoon.

Then we perform an experiment (which you have already done albeit accidentally): remove the silk from a caterpillar that is ready to form a cocoon.

Then we collect results and make a conclusion: Do you still have the caterpillar? You could continue to feed it and determine if it makes a cocoon. This is actually a very interesting question and I hope you will not feel too awful and see this "accident" as a opportunity to learn with your third grader. I hope this helps!

Note from ScienceLine moderator:

The person who sent this question recommends not to perform the experiment unless the life of the cocoon is saved.