One shows one's sad to split (4)
I believe the answer is:
tear
This clue is a double definition.
'one shows one's sad' is the first definition.
(as in shedding tears)
'split' is the second definition.
(I know that split can be written as tear)
'to' acts as a link.
(Other definitions for tear that I've seen before include "Drop secreted by the lacrimal glands" , "Move quickly; pull apart" , "Secretion of the lachrymal glands" , "A rip and a sign of sadness" , "'A rip, binge or drop of saline solution (4)'" .)