Support slowing down in speech that's exhausting (12)
I believe the answer is:
backbreaking
'exhausting' is the definition.
(I've seen this before)
'support slowing down in speech' is the wordplay.
'support' becomes 'back' (to back is to support or endorse).
'slowing down' becomes 'braking' (slowing down a vehicle).
'in speech' shows a homophone (sound like).
'braking' is a homophone of 'breaking'.
'back'+'breaking'='BACKBREAKING'
'that's' is the link.
(Other definitions for backbreaking that I've seen before include "Exhausting (toil)" , "Punishing" , "killing" , "(Of work) physically demanding" .)