Killing doesn't bring TRUE happiness. Happiness comes from following what God made you to be. This can be divided into two categories. The first is related to the "Image of God"- God made us all to be like Him, not in terms of His sovereignty, but in terms of His moral reasoning, social attributes (so I'm told), and intellectual capacity. The second is the path that God intends for you as an individual. God actually determines the interests and passions you will have, and He gives them to you for a reason, as part of His plan (see I Corinthians 12). Since murder is a sin, it doesn't bring us closer to what God made us to be, and so it is not only morally wrong, it is a way of ensuring unhappiness. Sadness is a natural part of human existence, but maybe sadness is distance from God and who He made us to be... and sometimes, it isn't.
(Final caveat- I have no idea how this framework applies to mental health issues)