You're not missing anything. Without space to build up momentum, the blade wouldn't cut it unless Mifune was stronger than the chain (and had more weight behind him than the chain could hold). Assuming a chain strength similar to iron.
And in regards to Grnmachine's character, I'm not a GM but I would like to raise some concerns/pose some questions. First the concerns.
His skin is as tougher than tempered steel, and protected against magic that he casts, and other forms of similar magic.
Considering that my original iteration of Krix had skin as hard as iron and was turned down by light because of his wide array of immunities/resistances, I'm not sure this would be something he would approve. Tempered steel itself can be twice as hard as iron, and Anthony's skin is harder yet. In addition to that, he's protected against fire, ice, earth, wind, water, illusion, light, and lightning magic. And exceedingly resistant to acid. That's more resistances than my character originally had, and even greater resistance to physical harm.
The next concern is with the time limits on your abilities. In most arena settings, for the purposes of measuring the timing of abilities that have a time limit, a single post is generally worth about 5 seconds. This means that your ice arrow would completely immobilize your opponent for 6 full posts, during which time you could do pretty much whatever you wanted to them (it also means you would only be able to use each type of magic once every twelve posts).
Then for the questions. These probably don't need to be answered in order to get accepted, but I tend to run through scenarios in my head and my curiosity demands they be asked (it'll also save time later on if I ever fight you so I know what the specific effects of his abilities actually are).
When you use the word "target", do you mean the thing he's aiming at or the thing the arrow hits? As an example, say he shoots the fire arrow at his opponent and misses for whatever reason. The arrow then goes on to strike the arena floor. Does it simply fizzle out because it didn't hit the thing he was aiming at, or does the entire arena floor now burst into flames?
175 mph is about 256 fps, which while faster than a recurve bow is still slower than modern compound bows. Based on your original post it seemed to me that you were wanting the arrows to be faster than even modern arrows can travel. This one was more of an observation than a question...
The wind arrow. As you have it now, if this arrow hit my character I would treat it as though it created a tiny tornado all around my character, but left the character himself untouched. Is that how you meant it?
The lightning arrow. This just makes lightning strike nearby, not where the arrow hits? If so, its only utility in combat would be as a flash-bang grenade.
The rain arrow. Is this just a big bubble of water that will essentially drown the person it hits?
