#!/usr/bin/perl

use strict;
use warnings;

my $PATH = 'http://a.com/a/b/c/d/e.json?something' . '/' . '/../../../
+';
$PATH =~ tr|/||s;
my $PREV = 0;
my $LEN;
for (;;)
{
  $PATH =~ s/\/[^\/]+\/\.\.//;
  $LEN = length($PATH);
  last if ($PREV == $LEN);
  $PREV = $LEN;
}
print $PATH;
[download]

I put the regex in a for(;;) loop, because adding global flag didn't do what I want:

$PATH =~ s/\/[^\/]+\/\.\.//g;