User blog comment:Blackendedsoul/Mihawk's Strength/@comment-3231264-20110725045650/@comment-1507483-20110725080356

Or Mihawk could throw(?) a flying slash that Blackbeard would not be able to avoid, making severe damage to him. He would only be able to absorb the slash thus making even more damage.

Also Mihawk might not be defenceless without his swords (and rember that he got more than one, so he would be albe to launch surprise attacks). He might have picked up something from Zoro's swordless styles, or even is able to use haki. Mihawk is the world's greatest swordsman and has been for a long time. He probably got a trick or two up his sleeve.