O. Ch. 321 – 8 Fine salt that got clumped together may be cut up into very small pieces.
The Mishna Verura (sk 31) explains ,because ein tochen achar tochen.
There is no issur of grinding something that was ground up once before.
O. Ch 302-7 Dried mud on clothing may not be rubbed (scraped) off on Shabbos
It is considered Tochen.
Why is there an issur tochen on mud? Originally the mud was sand , so the rule
of ein tochen achar should apply?
This question was asked by R.Akiva Eiger.( O. Ch. 302)
The Chazon Ish writes if the clumping was done by humans ,
(salt) the rule applies (ein tochen achar tochen)
if done through nature(mud) then there is tochen achar tochen.
The Shevisas Shabbos says that if it was clumped together and is very hard
(mud) the rule of ein tochen achar tochen is not applicable.
According to the Sh. S. there is reason to be machmir not to cut small
pieces of sugar cubes.