• Resolving /../ may lead to illegal or unwanted locations. The part before the /../ might be a symbolic link pointing to somewhere completely outside of the path you are changing
• Your solution, as mentioned by others, is not safe for leading ./, ../ or a range of ../../.. that would cause to go beyond the root

With you code safe-guarded against the above remarks, here is a compare of the methods mentioned in this thread plus the one I would use: Cwd::abs_path. Note that abs_path returns undef for non-existing path.

#!/usr/bin/perl

use 5.018003;
use warnings;

use Cwd qw( abs_path );
use Path::Tiny;
use File::Spec;

my @pth = qw(
    /a/b/c/d/../../../e
    /a/../b/./c//d
    ../scripting
    ./tmp
    /tmp/../../../tmp
    );

sub resolves {
    my ($p, $r) = @_;
    printf "%-20s -> %s\n", $p, $r // "$p does not resolve";
    } # resolves

say "OP";
foreach my $pth (@pth) {
    my @c = reverse split m{/+}, $pth; # /+ removes empty elements
    my @c_new;
    while (@c) {
        my $component = shift @c;
        next unless length ($component);
        $component eq "." and @c and next;
        if ($component eq ".." and @c) {
            my $i = 0;
            while ($i <= $#c && $c[$i] =~ m/^\.{0,2}$/) {
                $i++;
                }
            splice @c, $i, 1;
            next;
            }
        push @c_new => $component;
        }
    @c = reverse @c_new;
    $c[0] =~ m/^\.\.?$/ or unshift @c => "";
    resolves $pth, join "/" => @c;
    }

say "Cwd::abs_path";
foreach my $pth (@pth) { resolves $pth, abs_path ($pth);              
+  }

say "Path::Tiny::path";
foreach my $pth (@pth) { resolves $pth, Path::Tiny::path ($pth);      
+  }

say "File::Spec::canonpath";
foreach my $pth (@pth) { resolves $pth, File::Spec->canonpath ($pth); 
+  }
[download]

which produces

OP
/a/b/c/d/../../../e  -> /a/e
/a/../b/./c//d       -> /b/c/d
../scripting         -> ../scripting
./tmp                -> ./tmp
/tmp/../../../tmp    -> /tmp
Cwd::abs_path
/a/b/c/d/../../../e  -> /a/b/c/d/../../../e does not resolve
/a/../b/./c//d       -> /a/../b/./c//d does not resolve
../scripting         -> /home/scripting
./tmp                -> /home/merijn/tmp
/tmp/../../../tmp    -> /tmp
Path::Tiny::path
/a/b/c/d/../../../e  -> /a/b/c/d/../../../e
/a/../b/./c//d       -> /a/../b/c/d
../scripting         -> ../scripting
./tmp                -> tmp
/tmp/../../../tmp    -> /tmp/../../../tmp
File::Spec::canonpath
/a/b/c/d/../../../e  -> /a/b/c/d/../../../e
/a/../b/./c//d       -> /a/../b/c/d
../scripting         -> ../scripting
./tmp                -> tmp
/tmp/../../../tmp    -> /tmp/../../../tmp
[download]