'get to' means 'have to' or 'have got to'. And I learned that after 'get to', there should be infinitive, but I saw a sentence which is showing 'get to + ~ing' form, so I don't know how to translate it.
Here is the example. (from 'Baker's blue-jay yarn' by Mark Twain)
I've noticed a good deal, and there's no bird, or cow, or anything that uses as good grammar as a blue-jay. You may say a cat uses good grammar. Well, a cat does - but you let a cat get excited once; you let a cat get to pulling fur with another cat on a shed, nights, and you'll hear grammar that will give you the lockjaw.