The equivalent expression of “kill the goose that lays the golden eggs” in Chinese is “drain the pond to fish”. There is a story behind it.
It was the Spring and Autumn Period in the Chinese history (around 771 – 476 BC) during which China was a very loose federation of several states that were in war almost constantly. One year, the states Jin and Chu would be at war. The Jin Governor was very worried and asked Jiufan, one of his high rank officers: "The enemy outnumbers us. How can we win?” Jiufan replied: "All is fair in war. Deception wins the war." However, when the Governor told Jiufan’s proposal to another officer Yongji, Yongji said: "If we drain the pond to fish, there will be no fish for next year. If we burn the vegetation to hunt, there will be no animal for next year. Deception may help us win this war, but the next war it would not work again. It is not a permanent solution." Anyhow, the history says that Jin won the war using Jiufan’s strategy. However, after the war, Yongji received higher reward than Jiufan. Surprised officers asked the Governor: "We won the war because of Jiufan’s strategy. Why should Yongji receive more credit?" The Governor said: "Yongji’s thoughts are for the nation’s long-term interests; Jiufan’s proposal is only in response to a temporary situation. How can a temporary solution be put above the nation’s long-term interests?" Later, "drain the pond to fish" became an idiomatic metaphor for being too aggressive.