That's good, but somehow I just don't like seeing you needing to test with the m// operator, and then perform a nearly equal match for the substitution. To get away with invoking the regexp engine only one time instead of twice on each loop iteration, you can do this instead:

use strict;
use warnings;


my $test = "hello there ass\x08\x08wesome";

print "BEFORE: $test, ", "(length: " . length($test) . ")\n";

while ($test =~ /.\x08/) {
    $test = substr( $test, 0, $-[0] ) . substr( $test, $+[0] );

    #   Note: The preceeding line is the same as:
    #       $test = $` . $';
    #   but avoids using $` and $', side-stepping the global
    #   performance penalty associated with their use.

}

print "AFTER:  $test, ", "(length: " . length($test) . ")\n";
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