Ruin the source of profit. ‘Golden goose’ is reference to the old fairy tale of a goose that laid golden eggs, so if you kill it off, you no longer have a source of gold. Typically, used in reference to an idea or project that would end the status quo. (Compare to Throw a wrench into the machinery or Torpedo.)
“If you sell that part of our business, you will be killing the goose that lays golden eggs.”