When I change the content of VARCHAR(32) from 32 chars to 0, will it save some space? When I change the content of VARCHAR(32) from 32 chars to 0, will it save some space?

The reason I'm asking it is because I store a hash of 32 chars to check something but after a while I'll not use it anymore, so if it takes some of DB space, I might change this field to empty ''.

According to the manual, it takes 1b plus the chars for strings with 255 chars or less, but what if we already have some data and change it to empty, does it save some space?

I'm currently using MySQL with InnoDB engine.

PS.: I'm a beginner yet, please bare with me.
You are leaving the datatype at VARCHAR(32), correct?  But updating the value to be the empty string, correct?

A 32-char hash takes 33 bytes -- 1 byte length plus 32 hex characters (1 byte per character).

The empty string will take 1 byte -- 1 byte length, plus no space for any characters.

However...  You are deleting stuff out of the middle of blocks in the middle of the table.  So don't expect that zapping a million hashes will necessarily shrink the table by 32MB.  There are too many things going on with blocking, free space, reuse of free space, etc, to say anything more than "it will free up some space for future usage".

I don't know where you got the 1KB info in that link -- the length is 1 byte, not 1 kilobyte.