Origami structures can transform their form and function by changing the direction of their folds. This reconfiguration can enable multifunctional robots, but doing so requires a fast, robust, and repeatable actuation method. In this article, we present an origami gripper that uses dynamic transformation to change its kinematic behavior in less than a second. We characterize individual vertices to show that the transformation is predictable and repeatable for different designs and orientations. We then apply it to a multivertex template that is capable of a wide range of shapes and motion patterns, indicating that transformation can be generalized to complex and functional machines. To demonstrate this, we built a transforming origami gripper on a robotic arm to pick up multiple objects. Demonstrations show that the gripper can quickly reconfigure between three different grasping modes and has sufficient stiffness to engage with and lift multiple objects with distinct geometries.