Not exactly the same as this. EDIT: The solution to that question involves killing the horse. Shadowmere is immortal. This is not the same question.
I have gotten far enough in the Dark Brotherhood that I have been gifted with an immortal horse. The problem is, horses in this game seem more of a burden than a help, especially since Shadowmere seems intent on reporting any crimes he sees me commit.
Can I stable him somewhere so that he doesn’t follow me around every time I fast travel? Is there any way to get rid of this annoying (and creepy) horse?
Unlike the Shadowmere present in Oblivion, Shadowmere in Skyrim is not marked as Essential and can die, killing Shadowmere works for making it stop following you temporarily.
However, 15-20 days later, Shadowmere will respawn in the location of death, causing it to start following you again
Shadowmere just seems invunerable, as it heals at the same rate as damage is applied. The only way to kill Shadowmere is to apply enough damage to it so it loses all of it’s health in a single blow.
If your skills are high enough with a bow, you do not have to one shot Shadowmere. By sneaking and applying the 3.0x bonus and critical damage bonus you can use the Bound Bow or a Daedric Bow and use about 5 arrows to kill it. The same can be applied to all weapons or magic. Be sure to use weapons strong enough that Shadowmere’s health regeneration can not keep up with.