Translate the laws abbreviation of non-english speaking country in English written paper?

I seriously doubt the translated version you've shown would make any more sense to the reader and so would just leave them as is.

If the distinctions in the various abbreviations are important, you may want to explain them by including them in a spelled out fashion and mentioning that the abbreviation used comes from the original language. But the reality is, it sounds like the people reading your paper will be familiar with the laws of both countries, and so such information may be entirely superfluous.

The reference you are providing has a two-fold goal. First, it allows a curious reader to find the full text of the law. For that, you should provide a searchable identifier in the original language. Secondly, it should tell a lazy reader what the reference is about. For that, also provide an expanded translation to English.

In your case, I'd go with

SNR č. `11/1948 Zb = Slovak National Council law no. 11 / 1948 Collection of Laws.