You tried:     $string !~ s/\d{10}//g; and asked "why can't I just reverse it?" What you wrote did reverse something. But, as you say, not what you intended.

What you wrote means, "do s/\d{10}//g and then return success if it failed." Although that sounds a little funny and is not what you intended, it could actually be useful. Perhaps this will help you conceptualize what is happening:

if ($string !~ s/\d{10}//g) {
   print "String unchanged: couldn't find 10 digits.\n";
   # do stuff to deal with regex failure
}
else {
   print "All cases of 10 digits have been deleted.\n";
}
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Of course if we really wanted that effect, we would probably want to avoid the easy-to-miss "!" and say either of the following:

if (not $string =~ s/\d{10}//g) {
unless ($string =~ s/\d{10}//g) {
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To achieve what you wanted, check out the other responses which have offered good solutions.

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"Perl is a mess and that's good because the
problem space is also a mess." - Larry Wall