While the CW features DC's Deathstroke losing his eye thanks to Oliver Queen's Green Arrow, the actual story from the comics is far more personal. Rather than losing his right eye in a fight with another superhero, Slade Wilson's iconic injury was the result of his failure to protect and be there for his family when they needed him most. While there are a handful of different versions in the comics based upon the era/reboot, the core cause is still the same. Deathstroke was shot by the person who was closest to him.
In the original DC Comics' origin for Deathstroke, Slade Wilson enlisted in the United States military where he excelled at all forms of combat. Eventually, he met and was trained in the art of guerilla warfare by Captain Adeline Kane. Falling in love, Slade and Adeline got married and Kane was soon pregnant with their first child. However, Slade was chosen for a secret military experiment where 90 percent of his brain was unlocked, granting him an accelerated healing factor as well a near-mastery over his entire body. However, Slade soon became the mercenary known as Deathstroke the Terminator after he defied orders, though he kept his secret life hidden from his family.
As a result, when a criminal known as the Jackal kidnaps Slade's son Joeseph to force Wilson to give up the name of one of his clients, Slade refuses due to his personal code as a professional. However, this leads to Joeseph's throat being slashed, which severs his vocal cords. Discovering her husband's true line of work and his endangerment of their son, Adeline tries to kill Slade but only manages to shoot his right eye, forcing him to wear an eye patch. While the New 52 DC reboot alters the story to reveal that Slade lost his eye in a conflict with North Korean soldiers, the subsequent Rebirth reboot reverts back to Adeline shooting Slade after Joeseph's throat is slashed. While the story now features different foes, it still has to do with Slade putting his life as Deathstroke over his family, leading to him losing his eye in the process.
While this is what leads to Slade needing an eye patch and wearing his traditional half-mask, it is interesting that the wound never heals. Is his healing factor only good for minor bullet wounds and cuts, or is his lack of an eye a deliberate choice on Slade's part where he's consciously bearing a reminder of his past loss and failure? Either way, Adeline being the reason why he lost it is far more dynamic and personal as opposed to a superhero brawl where someone like Green Arrow or Batman is the cause.
As it stands, Slade Wilson's eye-patch and mask have become iconic parts of his depiction over the years. While the CW having Green Arrow stab Slade's eye out creates personal stakes and a major rivalry between the two, it's safe to say that the comics' origins are much more dynamic for Deathstroke on a personal level, serving as a constant reminder of one of his biggest losses and failures in his career as one of DC's deadliest mercenaries.