Project 1640 is a high contrast near-infrared instrument probing the vicinities of nearby stars through the unique combination of an integral field spectrograph with a Lyot coronagraph and a high-order adaptive optics system. The extraordinary data reduction demands, similar those which several new exoplanet imaging instruments will face in the near future, have been met by the novel software algorithms described herein. The Project 1640 Data Cube Extraction Pipeline (PCXP) automates the translation of 3.8*10^4 closely packed, coarsely sampled spectra to a data cube. We implement a robust empirical model of the spectrograph focal plane geometry to register the detector image at sub-pixel precision, and map the cube extraction. We demonstrate our ability to accurately retrieve source spectra based on an observation of Saturns moon Titan.