Just a Blade Witch going out for a joy ride on her sword demon she summoned!

"They [her shoulder eye/grafted arm and the eye on the hilt] are not directly connected but are related in that she got the arm in order to obtain the unholy amounts of strength to swing the sword around, they are drawn from similar pools of magick so to speak. That being said the sword can also swing itself around via magic but its like a stength check, having enough power to control it"

basically, a blade witch summons a sword demon from beyond into the mortal realm and has to bind it to her will by overpowering it or subduing it. There are many ways to achieve this (coercion, hypnotism, deception, negotiation) but in this case our blade witch Sophie grafted an arm imbued with unholy strength onto her so that she can physically overpower the summon sword, winning it's respect. The eye on the shoulder is a symbol of the pact forged between the two, and creates a psychic link between the two that can span vast distances, allowing for telepathy, sharing sight, and even a mode of transportation that works both ways. Very convenient