How can I get Shadowmere to stop following me?

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.

No, it is a bug. The horse dies for (but not for good) if you do that. She can also die if given a lot of damage at the same time. As from a dragon. She is not immortal, just heals herself fast. Jumping from very high cliffs kill her, because it is a lot of damage at the same time. You could also try to buy a new horse, ride on it, and then kill it. I have not tried yet, but if you own many horses the ones you are not using are stabled where you bought them. So maybe shadowmere would be stabled in the black pool next to the sanctuary.

*EDIT This buying/riding and then killing it works. Shadowmere stays where you dismounted her. Also, if she gets killed, she will respawn at the spot where she died and wait in the same maner. So if she dies, mark it, and come back to the spot in a couple of weeks.