I'll do my best to explain the approach using the 114BX. With the 114BX, there is a tip and ring connection (typically used for stereo 1/4" plugs) Additionally, there are internal spring connections that connect to the tip and ring terminals. When the plug is inserted in the 114BX, it breaks the connections between the tip and ring's springs.
When you plug a mono 1/4" plug into a stereo jack, the ring will be grounded because physically the plug's ground connection is connected to the sleeve of the jack and now the ring spring. The mono jack is ground at the location where a stereo jack would have a signal. So because of the insertion of the jack will separate the tip shunt from the tip spring, we can ground the connection going to the power section of the amp by leveraging the physical connection between the ring spring and the sleeve. We make a ring spring connection to the tip shunt which makes its way to the power amp section of the amp. The speaker will be dead quiet while the preamp signal is sent to another amp and/or mixer.
The best way I wrapped my head around this was to get a 114BX in my hand and use the continuity beep feature to see what's going on.