IF it is all you have to cut with........you can cut metal (stainless or carbon steel) but it will be, as you said.....messy. The term is called "hot-rodding" and it is best to use 6010 or 6011 electrodes.  If you have 1/8" rod, you probably only need 150 - 175 amps to cut 1/4" carbon steel but it will be messy and hard to follow any line you've laid out. Once you have the arc going, try to keep it (the arc) tight to the work and use a reciporcating motion to make a cut. You will probably only burn 1/2 of a rod as it will be glowing red-hot before you are thru with a cut. Be careful! I do not recommend you use your welder for this purpose, but it can be done.
Keep the flux on the rod. Usually you would be running single phase, 220 power for the welding machine you mentioned (lincoln 225 ac welder) so I would  say that the machine will be fine, but keep an eye on the lead as that will heat up a lot and the rubber insullation (on the lead) could melt so be careful.

you can use a air arc cutter  basicly a hand held stinger just like your rod holder but with a adjustable air nosel right behind the rod rod used is copper coated carbon you simply strick a arc push  buttin and it blows molten metal away excelent to air gouge a chanel in thick metal to repair cracks or but weld  ive got one id sell but id have to look up what its worth i use plasma now    sory about spelling they tell me there is spell check on ths thing but damed if i now how to do that need a 5 yr. old to teach how to use this thing!

I believe a Lincoln "buzz box" instruction book suggested soaking 6011 electrodes in water, then use them to cut ("selectively" melt) steel or iron.  It works but is not very pretty.  It won't harm your welder to do that.

Arc gouging can do a neater job but you need compressed air, and I am not sure but don't believe your 225 machine has enough power for it.

If you don't have a set of torches, you might find that an abrasive wheel made for a circular saw works pretty well for straight cuts.  Similar wheels are made to use with grinders.