Dear Ruth,
It's not unusual for children to mention wanting to die, at moments when they are very angry or have been denied something they want. It's not necessarily indicative of any serious pathology, but rather of momentary disappointment or rage.
On the other
handHand or foot spasms
Hand tremor, when children repeatedly say this, and particularly if they say it at times when they are not overtly angry or in other similar distress, it may be an indication of more difficulty. Because your son is going through a time of instability, it would be wise to seek an evaluation (not so much because of the single symptom you described today, but due to his overall unsettledness).
Your son may be depressed. How is he eating and sleeping? Because clinical depression is a physical problem with emotional symptoms, a child may feel sad or hopeless unconnected with specific cause...they then search for a reason to explain these feelings. That may be why your son is ruminating about his long-ago dead pet, the cruelty of life, etc.
Any time a child expresses a desire to die, as in your question above, you should take them to a pediatrician immediately and let them know exactly what the child has shared with you. He needs to be evaluated to make certain that he isn't truly suicidal. A doctor will be able to assess the situation, answer your questions, then provide a referral to a counselor or follow up appointment. Good luck!