The Executioner and Her Way of Life, Vol. 1 (manga)

The Lost Ones are strangers from another world, hailing from a place no one has ever heard of called "Japan." These wanderers have been associated with catastrophes since many years ago and the solemn duty of exterminating them without remorse falls to Menou, a young Executioner. But when her mission is complicated by a Japanese girl named Akari who refuses to die, Menou embarks on a peculiar journey to find something that can slay even an immortal who insists on traveling with her would-be-killer!

Volume 1 of The Executioner and Her Way of Life manga series by Mato Sato.