How do I copy sub category descriptions to a new budget, but not data?

Use Grow by Percent, with a -100% growth rate.

There isn't a copy function dedicated specifically to this, but you can achieve the right result by using the Grow by Percent feature.

Let's imagine you want to keep all the same sub category descriptions from Budget 2020 in Budget 2021 to act as a guide for your users who will be filling in the budget numbers.

Go to Data/Formulas > Grow by Percent, choose Budget 2020 as your source budget, and Budget 2021 as your target, and select the categories/accounts for which you need to copy over the sub category description.

Now check the Single percentage value for all selected departments box, select the appropriate departments, and enter -1 in the box. 

Now when you hit the Grow button, you are copying data with a growth rate of negative 100%, thus zeroing all your data, but keeping the descriptions.