In this work, a theoretical model for estimating the wax breaking force and wax removal efficiency of cup pig is developed. The proposed model is physically built upon orthogonal cutting and theoretically deduced from the slip-line field theory, allowing for the deformation of scraping element and rheological characterization of wax in the absence of adjustable parameters. The modeling results are experimentally verified. Multiple aspects of pig geometries, including clamping rate, scraping element thickness, original rake angle, straight part length and scraping element assembly, are elucidated, signifying some crucial implications in pig design. Moreover, due to the decent cleaning performance and low stuck risk, a two-cups-two-disks pig assembly is recommended for the studied case.