I am trying to draw a derivation for "Didn't the cat eat the mouse?" But I'm confused as to what the deep structure would be. "The cat did not eat the mouse" seems incorrect, since it is stating that the action did not occur, while the question implies that the action did occur. Thoughts?
In the very early days of transformational grammar, it was supposed that transformations could change meaning, and so your two examples could be given the same deep structure. The fact that they mean different things could be ascribed to a question transformation that applies in the derivation of one but not the other. In 1964, Katz and Postal published their very influential Integrated Theory of Linguistic Descriptions, which argued that the instances in which meaning-changing transformations had been proposed could be shown to be misanalyses, including the meaning-changing question transformation.
Katz and Postal proposed that the deep structures of yes-no questions differ from their indicative counterparts by being introduced with "whether", which appears explicitly only when the questions are complement sentences.
Many transformational grammarians adopted the Katz-Postal hypothesis that transformations don't change meaning, but seem to have taken it more as a convenient assumption than an empirical hypothesis (as Katz and Postal had proposed). In place of "whether", one often sees an abstract "Q" element assumed, as for example in McCawley's SPHE.