Get rid of tortuous JEE and heartless CAT! (5)
I believe the answer is:
eject
'get rid of' is the definition.
(I've seen this in another clue)
'tortuous jee and heartless cat' is the wordplay.
'tortuous' indicates anagramming the letters.
'and' means one lot of letters go next to another.
'heartless' says to hollow out the word (remove centre letters).
'cat' with its centre taken out is 'ct'.
'jee' anagrammed gives 'eje'.
'eje'+'ct'='EJECT'
(Other definitions for eject that I've seen before include "Force out violently" , "Evict" , "Oust" , "Boot out" , "Bail out" .)