the matrix - Do Morpheus and his crew kill potential Ones?

During the opening, we hear Trinity and Cypher talking to each other.

Cypher: We're going to kill him, understand?
Trinity: Morpheus believes he is the One.

Cypher: Do you?

Cypher says this in a way which may indicate there have been deaths before.

If so, were these deaths on purpose or accidental? I'm thinking he means taking a risk with the agents.

Answer

Morpheus and his crew don't kill potential Ones, but they have a tendency to get them killed.

During the Agent training program Morpheus tells Neo that

Every single man or woman who has stood their ground, who has fought an Agent, has died. But where they failed, you will succeed.

He also tells Neo that

We've survived by hiding from [Agents], running from them, but they are the gatekeepers, they're guarding all the doors, holding all the keys, which means that sooner or later someone is going to have to fight them.

That "someone" who will have to fight the Agents is obviously the One. All previous potential Ones were encouraged to stand their ground against an Agent but failed since they were not the One.

Cypher's comment that "we're going to kill him" stems in part from his belief that Neo will just be another failed One who will be killed when he stands his ground against an Agent. There's more to that, though, as I explain in another answer. First of all, Neo is relatively old for someone to be unplugged from the Matrix -- the comic Saviors proves that there is a risk of death when an older person is unplugged from the Matrix. Morever, when Cypher says that they're going to kill Neo he's in the act of betraying the crew -- this is a subtle way to cover up his betrayal by making Trinity expect Neo's death so that she won't suspect a betrayal. Furthermore, Cypher is in love with Trinity and was attempting to undermine Trinity's belief in the One.