Lyric discussion by JailBirdVagabond 

Cover art for Beat The Devil's Tattoo lyrics by Black Rebel Motorcycle Club

Also, just my thoughts, razors are commonly used to inflict self-harm so maybe the song's about destructive behavior in general? (addiction to drugs and self-harm)

Also in the first verse "Your body's achin', all your bones are breakin'", Aches and excruciating pains are commonplace in opiate withdrawals which furthers the heroin theme. Devil's tattoo may be the scars or "track marks" one gets from shooting up with syringes filled with heroin.