I'd back a face-saver but it reduces dividends (7)
I believe the answer is:
divisor
'it reduces dividends' is the definition.
The definition suggests a singular noun which matches the answer.
'i'd back a face-saver' is the wordplay.
'back' is a reversal indicator.
'a face-saver' becomes 'visor' (I can't explain this - if you can you should give a lot more credence to this answer).
'id' in reverse letter order is 'di'.
'di'+'visor'='DIVISOR'
'but' acts as a link.
Can you help me to learn more?
(Other definitions for divisor that I've seen before include "factor" , "Sort of number" , "B in A/B" , "Number under line" , "It will go in exactly" .)