Randomized algorithm for minimum cut
Yes, that's exactly the correct algorithm, and what you have produced is Karger's algorithm.
Since the algorithm is randomized, you can run it several time over in the hope of getting a better solution.  There is no guarantee that you will get the optimum cut, but you can make the error probability as low as you want to.
Here is Thore Husfeldt's illustration of it (cc-by-sa-3.0), 10 repetitions of the contraction procedure in Karger’s algorithm for minimum cut on a 10-vertex graph.  The 5th repetition finds the minimum cut of size 3.