There are few lines where I don't agree:

my $column_separator = ",";
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Better:

my $column_separator = qr/,/;
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...imaging someone wants to use "." as separator.

my $column_number = "3";
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Don't write numbers as text, write them as numbers (cut away those " chars).

Loading the whole file into memory might not be that good idea, imagine it's a 10 GB file. Why not parse it line-by-line?

open(FILE,"<","$file");
while (<FILE>) {
 my @columns = split(/$column_separator/);
 print $columns[$column_number],"\n";
}
close FILE;
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