"Down two hundred" in this context refers to scoring in bridge.
Being "down" in bridge means that your opponents have gained points, by preventing you from winning as many tricks as you and your partner said you would. Two hundred is a fairly serious sum for a single hand.
Six spades is a very high bid in bridge, and generally requires both very good cards (indicated by previous, lower bids) and intelligent play to succeed. The man who says this is implying that his partner possessed neither. Note that much of this is conveyed through intonation: the overall tone of this conversation establishes that the older man is frustrated and angry with the younger man's reckless/naive behavior.
"I thought I could do it, sir."
Here the younger man is trying to defend his decision; since he is speaking to an officer who outranks him (possibly his commanding officer, but I haven't watched the rest of the movie), he is trying to be polite and deferential. Since he did not, in fact, "do it", he is also being apologetic.
"Well, don't go off half-cocked again."
The older man accepts the implicit apology here and warns his partner not to bid as recklessly again.