Devices and related methods are disclosed that generally involve the selective deactivation of one or more engine valves. In one embodiment, a split-cycle internal combustion engine is provided in which a high-speed trigger valve is used to fill and drain a hydraulic tappet that forms part of a lost-motion system of an engine valve. A spool valve can be used to selectively disconnect the tappet from the trigger valve, thereby deactivating the associated engine valve (i.e., preventing the engine valve from opening). The devices and methods disclosed herein also have application in conventional internal combustion engines and can be used with inwardly-opening and/or outwardly-opening valves.