The 7.75 Damage Sword was a Mystic Sword sold by Marcus that dealt 7.75 attack damage, more than the 6.5 of a normal Mystic Sword at the time. It is no longer sold.
Every Mystic Sword now starts at 7.75 attack damage, and levelling it at the Mystic Well raises that further. The 7.75 Damage Sword therefore no longer has any advantage over other Mystic Swords. Its upgrade, the Doggo Book, has also been retired.