The suggestions to use the tiny abrasive disks with a high speed rotary tool or Dremel are a good solution.
The fragility of these thin (not reinforced) is an issue, but I rarely have one break while using them. I like the reinforced disks where it's not as easy to have a firm grip on the tool near the nosepiece, but the thin disks perform very well if the user doesn't try to steer them, let the disk grab in the cut or let the direction of the rotation feed (pull) the disk.
I can almost guarantee a high disk failure rate (that the fragile cutting disks will fail) if the workpiece is held in one hand and the grinder/tool is held in the other hand. But when the workpiece is held securely in a stationary vise/holder and the tool is held securely, the fragile disks perform very well and are a cost effective solution to making small cuts.
When the cutting direction is opposite the direction that the disk would travel if allowed to, the disks' fragility isn't a big problem.
BTW, there are diamond dust coated steel disks in the same size range as the small, thin cutoff disks that aren't fragile, and will cut/notch/grind various hard materials. An expensive diamond abrasive wheel shouldn't be used at high speeds on steel, but a $.80-.90 disk doesn't usually fall into that category (for most of us, anyway).
I got a blister pack from HF that included an arbor with a 1/8" shank and 4 or 5 diamond disks that only cost $4-$5 with an order of other stuff. I don't use them frequently, but I think I'm still using the first one removed from the pack.
These small power tools aren't impressive to look at, but when I encounter a fuctup fastener in a close location (where a torch or an air chisel aren't appropriate - junkyard work), the small tool is extremely worthwhile.
I've got a few old rotary tools that were made in the 1930-40s (0-1/8" and also 1/4" shank models) that still perform nearly as well as when they were new, and still perform the tasks that they were intended to.