That non-finite form saying expresses the idea that over the course of their relationship ("Carl always teased her") he would say those words, that mac-and-cheese was the only thing she knew how to cook: those are words he said when teasing her.
If you wanted to use a tensed form of the verb to say to express the same idea, you would have to say something like whenever or often in combination with the verb:
He always teased her about her cooking and often said it was the only thing she knew how to cook.
or whenever
He always teased her about her cooking and whenever he did so he said it was the only thing she knew how to cook.
or always
He always teased her about her cooking and he always said it was the only thing she knew now to cook.