You say you are trying to "split" the string, but it looks like you just want to remove unwanted characters. Everyone has pointed out variations on
s/[()"]+//g which certainly works.
Another way is the "tr" operator, which simply does character transliterations. In this case, you can "transliterate" the unwanted characters to nothing -- i.e. delete them:
my $string = '"(test123)"';
$string =~ tr/()"//d;
This is a simpler operation than regex substitution, so if your code needs to do this a lot, you could see a performance difference.