It means they can **designate** ..._without any [prior] trial or open process._ That is, **declaring** a group "undesirable" can be done secretly, without giving any reason.

It does NOT mean that the groups, or those who associate with them, won't have a "trial or open process" after they are arrested (although that might also be the case, but the article does not say that).

I hope this clears that up.  The phrase is adverbial to the verb "designate", not modifying the noun  "groups".