If I were to say I want to reduce the NUMBER of CIGARETTES I SMOKE, should I say " I am cutting down on SMOKING" or "I am cutting back on SMOKING"? Cigarette is a countable noun, so you need to say 'the number of CIGARETTES' (plural). The combination of 'amount' and a singular noun is used for uncountable nouns, for example 'I need to reduce the amount of beer I'm drinking.' As for the phrasal verbs, 'cutting down' is better: 'Cutting back' is usually used to talk about making economies in order to reduce expenditure. 'Cutting down' is more appropriate for talking about changing personal habits in a health context.

I generally hear "cutting back" more. "I'm cutting back on smoking/cigarettes." Smocking should be "smoking" & smock should be "smoke". Hope this helps!