In this specific case you could do it like this:

my $var ='[1,2]';
my @array = map { 0+$_ } split ',', substr($var,1,-1);
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If the array holds non-numbers (or you don't care that the numbers are saved as strings) you can remove the 'map { ... }' part.

However the CPAN module mentioned in earlier post would do this more safely and support more features.