Step 1 -- Iron into Manganese
Yes, it would immediately turn into manganese. As Franklin's answer and AlexP's comment states, the definiton of an element is based on the number of protons in the nucleus. To be a bit more accurate, it would be negatively charged chunk of manganese because the 26th electron is not taken away, meaning that it will be a mass of manganese ions.
Your magic reaction looks a bit like this: XFe + Magic -> X-1Mn- + 1H+
You've mentioned not really caring what happens to that proton, but it is there to balance the equation.
A brief look on Wikipedia reveals that Iron exists in nature with isotopes of 54, 56, 57, and 58 while the only stable isotope of manganese is 55.
Given what is stable for each element and their natural distribution via Wikipedia, if you did this to a random chunk of iron, you actually end up with a block of negatively charged manganese with 8.25% of it radioactive -- the parts not derived from Iron-56. The radioactive part will decay either into chromium (5% roughly) or back into iron (3% roughly)
The electrons will have to go somewhere so there will likely be a discharge into something or somebody. If the proton is just magically booted out physically as hydrogen ions, then the electrons will likely bond with those. Otherwise, it's probably discharging into the ground or into your person holding said iron.
The Sword of Air
Ansering your next question is much the same: By removing 18 protons from iron, it will by definition by oxygen. The resultant mess, primarily Oxygen-38 (56 - 18), will almost certainly instantly decay into other things in a highly energetic event that will likely kill anyone near the now transmuted sword. Your hapless swordsman victim will not have time to wonder where their sword went, the instantaneous radioactive decay will likely kill them.
As a side point, as the most probably steel sword is an alloy of iron and carbon, your sword will also drop carbon dust as the alloy is broken up. Not necessarily a lot of it, but enough.
Bonus: Transmutation Without Horribly Messy Death
If the goal for your atomic mage is to turn an iron sword into oxygen by messing with the atoms directly, then the aspiring mage will want to remove all three subatomic components -- protons, neutrons, and electrons -- so that the result is stable oxygen.
For refernce, a potential reaction could look something like this: 56Fe + Magic -> 40Ar + 16O
What happens to the argon's worth of bits is your choice, but this would lead to a sword vanishing into a poof of gaseous materials without killing your swordsman. Bonus is that both argon and oxygen are gasses so even if you kept the removed parts, it would still be a gas.