A fluid line device is for removing a fluid line from a body and may include a handle and a cutting head having a proximal end carried by the handle, and a distal end spaced apart from the proximal end. A fluid line channel may extend through the cutting head between the proximal end and the distal end for receiving the fluid line. The cutting head may also include a guide carried within the fluid line channel for supporting the fluid line therein during manipulation of the handle so that the cutting edge cuts body tissue away from the fluid line for removal thereof from the body.