Removing or leveling an old iron pipe embedded in concrete patio
Option 1(clean finish):Rough cut the iron, bar the concrete, and pour a top layer of grout or thicker layer of concrete.

Option 2 (rough finish, what you're doing): Rough cut with rip saw and finish with grinder.

Option 3 (rough finish, completely removes visible pipe): Clear adequate space around the pipe below the concrete for a cast iron pipe cutter

You're going about it the right way.

Option 2 details: Depending on your comfort with a rip saw, you may want to start with a masonry grinding wheel to smooth ~4" of the concrete around the iron to minimize risk of kicking against exposed stones (aggregate).

Using a medium gauge cutting blade(https://www.lowes.ca/reciprocating-saw-blades/lenox-es-2017-14-tpi-lazerreg-metal-cutting-reciprocating-saw-blade-5-pack_g2347551.html?searchTerm=lenox-lazer) trim off all that you can comfortably trim, follow up with a cut off wheel (https://www.amazon.com/Walter-ZIP-Cutoff-Wheel-Pack/dp/B00NFHM9E0)

From the 18" that you mentioned, this should take around an hour with out breaks. You'll need roughly two discs and two blades.

Option 1 is significantly more expensive and time consuming. 

-Start by deciding whether you'll use grout (minimizes the profile[depth]) or concrete, if you're using grout there are specifics that need to be considered, if you're using concrete, it's straight forward, minimum 2" pour.

-After you've decided which (or any other local option) you're going to use, use a rip saw, (or as another has suggested, a torch) to clear the pipe from the surface, leaving it partially exposed doesn't matter, as long as you can have it completely enveloped by the concrete. 

-Depending on the state of the slab, and your weather, you'll want rebar spaced at around 16" square from each other, figure out how much you'll need based off what you're expecting to add (min 4"), purchase re-bar and structural epoxy or grout.

-Mark off and drill the holes based off of what you're inset is (min 3") again at 16" square (more or less based off your weather)

-Pressure wash the surface, and clean out the holes from all dust, and sitting water

-Set the re-bar in to the holes with the grout or structural epoxy while waiting for the compound to cure/set...

-Frame off the slab for the pouring of the concrete and making sure it's moist but no sitting water (if it's grout, there can be sitting water for concrete) and finally perform your pour.

There isn't any more guidance that I can provide for this option, it can vary wildly based on what your local weather, building materials, expectations of quality, and more.

Option 3 can vary depending on the thickness of the slab, it can be time consuming, and requires renting of any tools you don't already have (SDS, SDS bits, cast iron pipe cutter). Again I can edit and provide more details.