If you want to replace for the content of $1 you must use /ee modifier to the regex.

$line =~ s/$regexp/$substitute/ee;
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One advice, its better to use a negated character class:

qr/throw "([^"]+)"/;
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Update I forgot to say that then you have to change the substitution pattern to something to be evaluated:

my $substitute = q{qq<throw ("$1")>};
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$anarion=\$anarion;

s==q^QBY_^=,$_^=$[x7,print