Systems for delivering prosthetic heart valve devices and associated methods are disclosed herein. A delivery system configured in accordance with embodiments of the present technology can include, for example, an elongated catheter body, a delivery capsule carried by the elongated catheter body, and two fluid chambers within the delivery capsule. The delivery capsule can be hydraulically driven between a containment configuration for holding the prosthetic heart valve device and a deployment configuration for at least partially deploying the prosthetic heart valve device. For example, the delivery capsule can be urged towards the deployment configuration when fluid is removed from the first chamber and fluid is delivered into the second chamber, whereas the delivery capsule can be urged towards the containment configuration to resheathe the prosthetic heart valve device when fluid is removed from the second chamber and delivered into the first chamber.