Remember that calling $dialog->Show pops up the dialog and doesn't return until the user has clicked a button. Well, you're calling that function twice. What you need to do is call it once, and save the result in a variable so you can test it as many times as you need to. Like so:

my $dialog = $mw->DialogBox (-title => "Delete", -buttons => ["Yes", "
+No"]);
$dialog->Label (-text => "Are You Sure you Want to Save?")->pack (-sid
+e => 'left');

my $result = $dialog->Show;
return 0 if $result  eq "No";
save() and exit if $result eq "Yes";

exit;
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