It's not really meant to take away suicidal thoughts, but if your suicidal thoughts are linked to stress and anxiety in any way, then yeah, it can take them away.
Klonopin and other benzodiazepines attach to receptors called GABA in the brain. The lower your GABA levels, the more stress, anxiety, and mood disturbance you might feel. Klonopin increases GABA to reduce these feelings. Just as well, it blocks electrical impulses from the nerve center of the brain, creating a calming feeling.
This is why, in a previous post on one of your other threads, I recommended Neurontin to you (generic name: Gabapentin). It's called GABApentin because it essentially does the same thing that Klonopin does in the sense that in increases your GABA levels. However, like I said before, even though it works on the same area of the brain, it does not work as well as Klonopin and other benzos as far as relieving anxiety, and it does also cause withdrawal if you've been taking it for a while. But having said that, it isn't a narcotic.