my @new = @array[join(",",@ARGV)];

You're building a string (using join) and then using that (one) string as array indices. That is certainly not what you want.

I can only imagine you want to use your arguments themselves as array indices, in which case it's straight forward:

my @new = @array[@ARGV];
[download]

You should be getting Argument "1,3" isn't numeric in array slice and an output of 12 though, so unless you've been mixing up different runs, I'm beginning to suspect your arguments 1 3 aren't being passed to the program.

Which would be another problem.