Assuming a recent version of Perl, I think your original code would work if the first sort were:

sort { (exists $a->{vtype_ug}||0) <=> (exists $b->{vtype_ug}||0) }
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You've got the compare function giving the opposite result than desired, but yes, it does work (in 5.8.8, at least), with this code:

@sorted = sort { (exists $b->{vtype_ug}||0) <=> (exists $a->{vtype_ug}
+||0) }
   sort { $a->{total_rate} <=> $b->{total_rate} }
   @arr;
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Actually, there's no need for that || 0 as exists returns a boolean, thus, that's safe to use as 0 when it returns false. So the next works too, without any warnings:

@sorted = sort { exists $b->{vtype_ug} <=> exists $a->{vtype_ug} }
   sort { $a->{total_rate} <=> $b->{total_rate} }
   @arr;
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