OR-Library is a collection of test data sets for a variety of OR problems.
A full list of the test data sets available in OR-Library can be found here.
OR-Library does not have any test problems for min-cut clustering.
However test problems for min-cut clustering are available from here
These test problems are some of those solved in E.L.Johnson, A.Mehrotra and G.L.Nemhauser, Min-cut clustering, Mathematical Programming, vol. 62 (1993), pp133-151.
Note here that the min-cut clustering problem is sometimes called the graph partitioning problem.