To "cut back" may be "reduce", but "cut right back" would have to do with the movement of a car in traffic or a sports player as s/he is getting into position. A scrub may be "cut right back" into a desired position or shape.

thank you

It means 'to reduce' or 'to economize' (such as when you do not have much money). It can also be used to refer to foliage; you 'cut back' a shrub.