As you might know, Jesus willingly submitted himself to crucification and therefore death on good friday. If he had not done so, nobody else would have died. Hence does that mean that Jesus committed suicide and is henceforth sinful as he took his own life and the net loss of life due to his voluntary crucification would always be +1?
I believe your question is focused enough that few of the many sects represented on this site would fundmentally disagree with my answer, so I'll provide it.
Suicide, as you point out, means you take your own life. It is an active choice (even when mental issues such as depression are involved1). But where do we draw the line? If someone sits on train tracks knowing a train will come because they no longer wish to live, it's suicide. If someone throws themselves on a grenade to protect others, it's not.
In other words, suicide is defined more by the reason for dying than it is the act of dying.
Jesus had no desire to die. His prayer in Gethsemene proves that. "Father, if thou be willing, remove this cup from me: nevertheless not my will, but thine, be done." (Luke 22:42)
Of the many things that made Jesus the Son of God, one is that He had the choice to live. All other people who have and will live on earth only have the choice to die. We can, if we so choose, decide the moment of our deaths. But none of us, facing that moment, can choose to avoid it. We can choose not to die in that we choose not to raise a gun to our heads today. But we cannot choose to live once the trigger has been pulled.
But Jesus could choose to live.
At any moment, while hanging on the cross, He could have commanded the angels to lift him down. He could have commanded his wounds healed. He could have chosen to live (and was even once tempted by Lucifer to abuse this power, Matt 4:6). But the atonment required a willing sacrifice — a person willing to throw themselvs upon the proverbial grenade to protect others — and that choice had to be absolute in every possible way. With his last breath He could have chosen to live, but the rest of us were more important to Him than His own life. He allowed Himself to die that we may live. That is the essence of love.
A willing sacrifice is an act of love and respect for others. Suicide is inherently selfish, an effort to remove oneself from burden or responsibility.2
Why a person chooses to die determines whether or not the act was one of suicide or sacrifice.
Therefore, no, Jesus did not commit suicide. He remains guilty of no sin. And having lived a perfect life, He has the privilege of judging all sin. And while I do not understand all things, I believe I understand this well enough to be content with my faith.
1 As we, today, work to better understand suicide and the influences in a person's life that might lead to it we risk two extremes of opinion. One extreme is to blame the victim, the person committing suicide, suggesting no influence could have culpability. The other extreme is to blame the circumstances, suggesting the victim is in no way culpable. For the sake of simplicity in this answer, since the person had to (e.g.) pick up the gun and no influence could, the victim always has some culpability. But in my opinion, the greater judgement will be upon those who participate in the influences. The victim may have stopped loving his or herself — but no scripture says we must do that straight out. On the other hand, the infuencers stopped loving their neighbor, and there is a scripture that specifically commands that.
2 This is a bold, callous statement that is in many ways lacking in compassion. I offer my apologies to anyone who has been touched by the tragedy of suicide. My intent was not to reopen any wound, but only to be clear about the difference between sacrifice and suicide. In my opinion, only Christ can judge if any person has truly committed suicide. Only He can know what influences were in any individual's life.
A local lad was leaning over a pool table to play his shot when his necklace tipped into sight - a cross on a chain. One of his friends said, "Why are you wearing that? If your Father had been shot dead, would you wear a bullet on a chain round your neck?" The lad thought for a second then replied, "If he'd taken that bullet for me, then yes, I would."
That's a true story, told to me by the church minister of that lad's mother. It makes a powerful point, relevant to your question. A person who chooses to die in order to save another, does not commit suicide. They perform an heroic act.
In the Bible, Jesus is called a sacrifice, the Lamb of God that takes away the sin of the world (John 1:29). He is spoken of as willingly going to the cross to die as the only perfect substitute for sinners there has ever been. That was the point of leaving heaven to be born to Mary. He came to die. He was in control of the timing of the event and ensured satanic opposition did not precipitate events too soon.
At just the right time, he allowed events to take their predestined course and did not resist them. The charge that got him crucified was a political one, that he claimed to be King of the Jews, which, to the Roman Empire, was treason. He was not put to death for any religious reason, although the religious Jews would have stoned him to death for claiming equality with God. Jesus prevented them stoning him on several occasions (see, for example, John 8:54-59).
To all appearances, he was put to death as a political usurper, but he actually died in order to do for us sinners what we could never do for ourselves - bear the punishment for our sins to pay back to God the debt of our sins. It was a transactional death, designed from before creation (1 Peter 1:20) to restore that which was lost to sinners. It was God, in Christ, who came down from heaven to become that atoning sacrifice. Allowing yourself to be put to death so that others can live is bravery indeed, not the attempt at escapism that is suicide.