Three-dimensional texture-based volume rendering is a technique that treats a 3D volume as a 3D texture, renders multiple 2D view-oriented slices and blends them into the frame buffers. This technique is thoroughly developed in computer graphics and medical visualization, and widely accepted due to the advancement of computer hardware. This research aims at developing fast parallel slice cutting and partial exposing algorithms used in real-time 3D-texture-based volume rendering for image-guided surgery and therapy planning. In texture-based volume rendering, a large amount of slices are needed to render the volume to achieve high quality image, but for real-time interactive volume rendering, the computation time is critical. Instead of repeating the cutting algorithms for each slice against the volume data as conventional cutting algorithms do, the slice cutting algorithm developed in this paper applies the cutting only to the initial slice, and gets the slice vertexes and 3D texture coordinates for all the others based on the distance between the current slice and the initial slice. The new algorithm dramatically reduces the computation time for slice cutting, and eases the generation of sectional view for a volume. Partial exposing is another useful technique used in volume visualization to reveal important but hidden information. Two depth-based partial exposing algorithms are developed and implemented in this paper. Both partial exposing techniques can work with arbitrary complex, but convex, shapes of cutaway object, and their implementations maintain the interactive frame rate for 3D texture-based volume rendering without apparent performance decline compared to non-cutaway rendering.