The demon Jashin-chan has been summoned to Earth by Yurine Hanazono, a girl with a knack for the occult. Unfortunately, Yurine does not actually know how to send Jashin-chan back to Hell. Now stuck on Earth, she must live at Yurine's apartment as her familiar. The only way for Jashin-chan to return would be to kill her summoner, but this is easier said than done for the incompetent demon. Since Jashin-chan is immortal and can regenerate her body, Yurine does not hold back in attacking her with a range of weapons, punishing her in gruesome manners for her evil schemes. Jashin-chan is also often visited by her demon friends: the kindhearted Gorgon Medusa and the energetic minotaur Minosu, who seem much more well-behaved in contrast, and disapprove of her plans to kill Yurine. Jashin-chan Dropkick is a comedy focusing on these two reluctant roommates and their bizarre antics as they get by with their cat-and-mouse relationship.

Jashin-chan is a demon who was summoned by Yurine Hanazono, a gothic looking girl. Unable to return home as the relevant spell was not included in the summoning grimoire, Jashin-chan resorts to violence to liberate herself from her earthly shackles. However, this is easier said than done, as Yurine is no weakling herself. She in fact possesses formidable physical power and uses it to massacre Jashin-chan in a variety of ways, be it shoving her arm in a blender, spreading her intestines across the room or even cooking her. Though these actions would be fatal to anyone without the ability to regenerate, Jashin-chan isn't exactly undeserving of this treatment. Stuck with each other, Yurine lets Jashin-chan live with her in exchange for work around the apartment, and this cohabitation results in situations where, more often than not, Jashin-chan ends up in pieces.

Subaru Mikazuki is a 23-year-old mystery novel author, major introvert, and an awkwardly shy person. He would much rather stay home to read a book than go outside and interact with others. Further exacerbating this life of solitude, his parents tragically died in an accident many years ago, leaving him alone in the world. One day, while giving offerings at his parents' grave, Subaru runs into a small grey and white cat named Haru, which he ends up taking home with him. Subaru, however, has never taken care of anyone else in his life—can he even take care of a cat? Haru is grateful toward Subaru, as he gives her all the food she wants—a luxury for a cat who is used to a rough life on the streets. But she notices that Subaru can't even seem to take care of himself! Will she be okay with this dunce? Doukyonin wa Hiza, Tokidoki, Atama no Ue. tells the story of an unlikely friendship between a human and a cat who try to foster an understanding with each other.