I think you want truncate, as in the untested code below:

use autodie;
use Fcntl ':flock', ':seek';
open my $fh, "+<", "mail";
flock $fh, LOCK_EX;
my $text = do {local $/; <$fh>};
seek $fh, SEEK_SET, 0;   # Only needed if you're going to write.
truncate $fh, 0;
close $fh;
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