Sink like a stone - Sink like a stone simply means to fail completely. There is only one straight forward meaning, so I don't feel any need to elaborate. So lets just move on to have an eye on the sample usages.
1. The project tiger seems to have sunk like a stone, tigers are being killed even today, ridiculously.
2. I pray that ISC does not sink like a stone, it is a nice approach for the students and I love this place.
3. Rama did not do her job full month, and at the last day, she worked all night, but sadly, the stone sank.
4. Abhijeet was only a show-off guitarist, he did not know how to pluck, so on the show night, the stones sank.
5. There have been many initiations to eradicate poverty in the country, but most of them sank like a stone.