I have a group of strings like:

[[something and something [[like this]] and this [[but]] here is [[what]].]] [[another big string [[with other]] substrings.]]

string1 => something and something [[like this]] and this [[but]] here is [[what]].
string2 => another big string [[with other]] substrings.

For the SPECIFIC example you posted, this works.

$ echo "[[something and something [[like this]] and this [[but]] here is [[what]].]] [[another big string [[with other]] substrings.]]" \
| perl -nle 'print "$1\n$2" if (/\[\[(.*\]\]\.)\]\]\s+(\[\[.*\.)\]\]/);'
something and something [[like this]] and this [[but]] here is [[what]].
[[another big string [[with other]] substrings.
$

Yes, that works, but the problem is that the strings change in size and in number of substrings, and the .]] also may change!

Another example:

[[something is something]] [[and then I was [[wondering]] why is  [[this like so]]]] [[anyway I think [[that]] I [[can]] go to]]]] [[blabla]] [[bla bla [[foo]] [[bar]]]] [[foobar]] [[not]]

[[something is something]] [[and then I was [[wondering]] why is  [[this like so]]]]

int foo(char *src)
{
   char dest[80][120]={0x0};
   char *p=NULL;
   char *q=NULL;
   int line=0;
   int count=0;

   for(p=src, q=dest[line]; *p; p++)
   {
        if(*p=='[') count++;
        if(*p==']') count--;
        if(!count && *p==']')
        {
              line++;
              q=dest[line];
             
        }
        if(!count) continue;
        *q=*p;
          q++;
   }
}

So what specifically is the delimiter and the action desired?

In your first example, the "[[sub strings]]" were kept in the broken out string 1 and string 2. Are all the enclosing [[ and ]] ultimately enclosing separate strings that will be recursively knocked down? In your example, you only showed one break on the ".]]"