Slowdown things happen in three main ways
1) You buy a controller (usually third party) that will rapidly press the start/pause button for you, probably bringing up any menus or playing sound effects in the process.
2) Your device has a slow processing mode and your cheat cart or whatever trips you into that and with it the rest of the console. The GBC is probably a good example (
https://bgb.bircd.org/pandocs.htm#cgbregisters ). This might not work depending upon the system and architecture.
3) You find some code that is run all the time and inject your own in there as busywork (or maybe shutdown/sleep if you like saving power) such that the rest of the game.
Sometimes this will crash things, sometimes it will make things hard to control, sometimes it will do nothing at all (the game might be built to handle it or handle things in such a way that your instruction flood does nothing) and sometimes it will actually add just enough load to the CPU that the game itself chugs along in slower speed than normal and thus acts as slow motion. This unreliability, and inability to really fine tune things, means few ever really use it and thus it will probably not be missed.
If however you have the code to find a nice vblank interrupt routine, or core loop of the game, like you would have to be able to be reasonably able to inject cheats* into random games without external code running all the time or whatever you can hack (see the 3ds, wii, or indeed the PC)
*if you are good enough that you can reliably alter instructions (change sub life count to add, reliably determine and alter IF ELSE...) with an automatic tool that is not a prebaked database of injection points instead of injecting something constantly writing RAM then you are good enough to reliably add proper slowdown, and probably win a nobel prize for computing as you probably just made AI (or at least something 90% of the way there) and likely changed the whole world of computing forever on various fronts even if not.