First, your regex wasn't matching. For example, \w does not match '[' as would be necessary for your expression to succeed. And \w does match '_' which complicates things since you have '_' as a char right after the variable you want to interpolate.

Second, if you are using use strict; (recommended) and variables declared with 'my', you need to use the approach for lexicals given on the page you mention:

my @Val = qw(aaa bbb ccc);

my $str = 'TESTDATA_BETA$Val[1]_DEFL$Val[2].$Val[0]';

if ($str =~ s/(\$[^]]+\])/$1/gee) {
   print "$str\n";
}
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This assumes all the interpolated values are array values. If that is not the case, a different approach will be needed in the first half of the regex. Perhaps something like: s/(\$[a-zA-Z0-9[\]]+)/$1/gee which also works with the example data you gave.