Assuming you have appropriate input, the code you've posted will function. warnings suggests you should be typing $date_array[2] in place of @date_array[2] (the latter is actually a slice instead of a scalar element), but this should not affect your result. Are you sure you are feeding it what you think you are? The following works as I would expect:

#!/usr/bin/perl
use strict;
use warnings;

my $date = '1/2/03';
my @date_array = split(/\//, $date);
my $new_date = join('-', $date_array[2], $date_array[1], $date_array[0
+]);
print $new_date;
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