I am the mighty world-destroying Time, now engaged in destroying the worlds. Even without You, none of the warriors arrayed in hostile armies shall live.
Bhagavan is re-iterating the fact that the jiva is a mere instrument to get the Lord's work accomplished. He is Time and Time is the destructive force in this context.
Destruction in Vedanta is not negative. Unless the old dies and gives away the new cannot come. When we mature in our evolution , we die to the old and vain bad traits. So Death is only Change. And the Lord says when a Time comes that the evil has become so much, then destruction becomes essential. The Lord is ever merciful even to the evil. Even in their destruction he is only paving the way of a better life for them to start with.
So as destruction he has now appeared in Kurukshetra. Even without Arjuna the Lord's purpose will be undertaken.
Therefore, stand up, and obtain fame. Conquer the enemies and enjoy the flourishing kingdom. Verily by Myself they have already been slain; be a mere instrument, O left-handed archer.
Arjuna was like merely seeing shadows in a crowd seen in a wall painting. Even though the warriors in the war are boasting about their strengths , they have no reality. Their fighting will be like the wars fought on a movie screen, where there are neither people nor weapons. The spectator forgetting that he is watching a movie gets identified with the objects in the screen and then gets affected. Similarly the shadows of warriors are only "shadows" but they think they are fighting and killing, but in reality they are mere shadows. Therefore Arjuna, get up and be an instrument, and take fame, for I have already accomplished them.
Drona, Bhisma, Jayadratha, Karna, and other brave warriors- those have already been slain by Me; you do kill; be not distressed with fear; fight and you shall conquer your enemies in battle.
Drona, Bhisma and so on all of them were like ghosts. Ghosts appear only in darkness, but where there is light they disappear. Likewise these enemies will disappear once you bear courage and begin fighting . Therefore get up and fight.
On the other hand if you escape and take to renunciation, the fact that you did not fight will haunt you all life. You will never be able to do anything successful. Hence even if you want to become a sanyaasi do it after fighting the war and securing the kingdom. That is true dispassion which is given up though one has it or is capable of getting it. You will then be worshiped as a true renowned sacrificer and a revered sage. If you run away now you will be called a coward. Therefore pick up you bow and fight the war, for I have already fought them for you.
The above three Slokas are not only meant for Arjuna. The implied meaning is what will happen will happen with or without us. We think we have accomplished and done this or that, but Bhagavan says we are mere puppets and the Lord accomplishes everything through us. That is why in the Vishwa Roopa it was said the Lord has many hands and feet. But out of ego and sense of individuality if we will not act or think ourselves to be very good actors, both ways we will perish as it will only deepen the individuality (our ignorance) and keep us in Samsara.