No need for a plumber.
There should be a trap under the sink, either a downward curved section of pipe ("p", "j", "u" trap) or a larger cylindrical component (bottle trap). All of these are intended to capture large or dense solids so they don't travel further into the drain and cause a blockage in a section that's harder to access.
Traps are designed to be easily undone, and reassembled, by hand or with minimal tool use. There will be a small amount of water inside so place something underneath to catch it - bucket, dish, old towel. If you find the locknut too stiff for you, use an adjustable wrench or try wrapping a towel over the contours and squeeze as you twist.
I still don't see how the liner could have grown too large to just stuff into a bin though. Well, now you know not to cut anything up in a sink with the water running.