Let's summarize all the suggestions
两败俱伤 = "both lose, both get hurt". It is the most fitting idiom for "lose-lose situation"
玉石俱焚(burn together with the enemy) , 同归于尽 (die together with the enemy) are more fitting for describing "mutual destruction"
鱼死网破 (the fisherman loses his net and the fish loses it's life), is a lose- lose situation but the main ...
"The future of us start here"
It is a slogan (口号).
A slogan is:
a short and striking or memorable phrase used in advertising.
a motto associated with a political party or movement or other group.
Slogans come and go, the more memorable ones may be adapted by the public and become part of the daily vocabulary. The one you see here isn't ...
Is it an idiom?
Is 金口难开 a chengyu? No I don't believe that it is. On one side of the coin 金口难开 could be considered a construct; in this case a phrase made-up of two different words: 金口 & 难开. In fact, 金口难开 doesn't really have an entry in any readily available dictionaries. Interestingly enough, though, the expression does show up as an example ...