What I found was that you need to use opposing force. Use a wedge or something of the sort to put pressure on the cut to push it apart and then you can cut the rubber with a knife, until you come to some wire and then the recip saw will work or any type of saw.
We cut a bunch by setting an old iron mowing machine wheel in the center of the tire, but yet it was big enough that it wouldn't fall thru' the rim hole. We had a pipe run thru' where the axel would go with a coller on the pipe, that turned around that pipe, attached to a long arm and a sharp piece of iron (like a knife blade) attached to the arm, where we wanted to make our cut.
The arm extended out beyond the blade and the tire it's self. You just walked around and around, pushing or pulling on the arm and the blade always followed the same path and the iron wheel put enough pressure on the tire that the cut would open slightly with each pass and the blade could then cut deeper, without hanging up on the edges of the rubber tire. We never used oil but I'll bet oil or liquid soap would help also.
Not much effort needed, just a little time. And not much of that. :wink: