Hi shahrzad,I think 'sink a steamer' is the act of taking a shit.

Although the other answers are correct, there's a little more to the phrase. A steamer can also mean a steamboat or steamship; a boat run by steam power. These are usually large boats, so if a steamer (steamship) sinks, it's quite a huge event! Also, if something is umm... "freshly produced" and warm, then it naturally gives off steam (like freshly baked bread). So a thing which produces steam is also called a steamer. So that's another image behind the expression.

Taking a shit. Going number 2 (peepee is number 1).

The act of taking a shit.

Thanks all.