I recently had to cut some 6.00-16 tyres from wheel rims. I used a Sawzall with a demolition-toothed blade to cut out a big 'U' in the rubber down to the steel wires/belt, then an angle grinder with a metal cutting blade to nip through the steel part once I prised it just clear of the wheel rim using two large screwdrivers. Worked well: some mess of rubber granules from the saw, and a little acrid smoke from the grinder, otherwise no problem at all. 
Unless you want a clean edge, the Sawzall worked well. 
I've used a non-slip tape on steps and it works really well. 
Like this: 
https://www.amazon.com/Slip-Guard-No.../dp/B01HQXNBHW
Mike