Accurate and efficient simulation tools are essential in robotics, enabling the visualization of system dynamics and the validation of control laws before committing resources to physical experimentation. Developing physically accurate simulation tools is particularly challenging in soft robotics, largely due to the prevalence of geometrically nonlinear deformation. A variety of robot simulators tackle this challenge by using simplified modeling techniques -- such as lumped mass models -- which lead to physical inaccuracies in real-world applications. On the other hand, high-fidelity simulation methods for soft structures, like finite element analysis, offer increased accuracy but lead to higher computational costs. In light of this, we present a Discrete Differential Geometry-based simulator that provides a balance between physical accuracy and computational speed. Building on an extensive body of research on rod and shell-based representations of soft robots, our tool provides a pathway to accurately model soft robots in a computationally tractable manner. Our open-source MATLAB-based framework is capable of simulating the deformations of rods, shells, and their combinations, primarily utilizing implicit integration techniques. The software design is modular for the user to customize the code, for example, add new external forces and impose custom boundary conditions. The implementations for prevalent forces encountered in robotics, including gravity, contact, kinetic and viscous friction, and aerodynamic drag, have been provided. We provide several illustrative examples that showcase the capabilities and validate the physical accuracy of the simulator. The open-source code is available at https://github.com/StructuresComp/dismech-matlab.git. We anticipate that the proposed simulator can serve as an effective digital twin tool, enhancing the Sim2Real pathway in soft robotics research.