We introduce a technical approach for reducing three-dimensional infrared (IR) spectroscopic data generated by integral field spectroscopy or slit-scanning observations. The first part of data reduction using IRAF presents a guideline for processing spectral images from long-slit IR spectroscopy. Multichannel image reconstruction, Image Analysis and Display (MIRIAD) is used in the later part to construct and analyze the data cubes which contain spatial and kinematic information of the objects. This technic has been applied to a sample data set of diffuse 2.1218 ${mu}m$ $H_2$ 1-0 S(1) emission features observed by slit-scanning around Sgr A East in the Galactic center. Details of image processing for the high-dispersion infrared data are described to suggest a sequence of contamination cleaning and distortion correction. Practical solutions for handling data cubes are presented for survey observations with various configurations of slit positioning.