no matter what; wouldn't say it even if my mouth were torn apart
Used with a negative sentence to emphasize that one would never say or reveal something, no matter what. Often followed by 言えない or similar negative verbs.
See also: 口が裂けても言えない
I wouldn't tell the truth no matter what.
I could never reveal his secret, no matter what.
A fixed idiomatic expression literally meaning 'even if (my) mouth were torn apart.' The exact origin is uncertain, but it vividly conveys the idea that one would rather suffer physical harm than speak.