Can I get all min-cuts after executing Push-Relabel?
I assume that your question is "Do I find all min s-t-cuts this way?"

I believe the answer is no. Note that there may be an exponential number of minimum s-t-cuts (connect vertex s to vertices {1,2,3, ...,n} and then each of these are 
connected to vertex t -- then there are 2^n min-s-t-cuts). 

The way that I know for sure to enumerate all min-s-t-cuts is to recursively enumerate all directed cuts in the residual graph after the contraction of all
strongly connected components. This algorithm can produce
each cut in linear time per cut. If you need a detailed description of the
enumeration algorithm I can provide to you the pseudocode.