You gave value to your elements that assume the elements can be ORed together, but subs element and transmute assume otherwise. The following would remove this ambiguity.

use constant Earth => 0;
use constant Air   => 1;
use constant Fire  => 2;
use constant Water => 3;

my @elmt_name = qw( Earth Air Fire Water );

# Gorgon::element
return $elmt_name[ $self->{element} ];

# Gorgon::Euryale::transmute
$elmt = ($elmt + 1) % 4;

# Gorgon::Stheno::transmute
$elmt = ($elmt - 1) % 4;
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Also, I find it funny that element accepts a number when used as a setter, but returns a string when used as a getter.