Advances in soft robotics and material science have enabled rapid progress in soft grippers. The ability to 3D print materials with softer, more elastic materials properties is a recent development and a key enabling technology for the rapid development of soft robots. However, obtaining the desired mechanical properties (e.g., stiffness) of the soft joints and information about the parameters to select in 3D printers is often not straightforward. In this article, we propose the use of interpenetrating phase composites (IPCs) materials with mathematically generated topologies based on triply periodic minimal surfaces for the development of soft grippers with desired mechanical properties. The flexible joints of the gripper can be realized through two or more phases that are topologically interconnected such that each phase represents a standalone cellular structure. As a case study, we present the design and development of a two-finger soft gripper as an example to demonstrate the application scenario of our approach. The flexible parts with desired stiffness values are realized by using IPCs materials in which the reinforcement distribution can be regulated on the basis of mathematical models. We characterized the properties of the material through a set of quantitative experiments on IPCs material specimens, and then we realized qualitative grasping tests with the gripper and a set of objects with different shapes and sizes. We showed that by properly regulating the properties of IPCs material it is possible to design modular grippers with the same structure, but different closure motions. Grippers can be customized for different tasks by easily assembling and disassembling fingers.