Yes, you are only splicing the sheep out of a copy of the array. To remove it from the original array, you must continue referring to it by reference.

sub RemoveSheep {
    my $self = shift;
    my $obj = shift; # This is the sheep object

    my $field = ${$self->{field}};
    my $sheep_ref = $field->Sheep;

    for my $index (0..$#$sheep_ref) {
        my $sheep = $sheep_ref->[$index];
        if ( $sheep == $obj ) {
            print "Before Splice: " . @$sheep_ref . "\n";
            splice @$sheep_ref, $index, 1;
            print "After Splice: " . @$sheep_ref . "\n";
            last;
        }
    }
}
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- Miller