同意前面几位老师的看法，比如下面一句摘自《张道真英语用法》：

Our advice is that the company cut down its expenses. 我们的建议是公司缩减开支。

句中的cut down its expenses 与你的句子中的 cut down on your spending 用法相当，意思也相似，你的句子中用的是 cut down on，《张道真英语用法》用的是 cut down。

Longman Dictionary of phrasal verbs：

cut down：动词+副词

cut down on：动词+副词+介词，无被动语态。

我认为：

cut down的含义较多，有“砍倒，杀死，减少、降低、缩减、缩小”等含义，主动语态和被动语态均可用。

cut down on的含义仅为“减少”，无被动语态。

当表示“减少”时，如果用主动语态，则两者可互换。

一点看法，不一定对，请专家批评指正。

cut down phr v 【REDUCE】 to reduce the amount of something cut sth⇔down Installing double-glazing will cut down the noise from traffic. cut down on By getting the design right, you can cut down on accidents. 【EAT/USE LESS】 to eat, drink, or use less of something, especially in order to improve your health I've always smoked, but I'm trying to cut down. cut down on Cut down on fatty foods and alcohol if you want to lose weight. 【TREE】 cut sth⇔down to cut through the main part of a tree so that it falls on the ground 【KILL】 cut sb⇔down literary to kill or injure someone, especially in a battle Hundreds of men were cut down by crossbow fire. 【REDUCE LENGTH】 cut sth⇔down to reduce the length of something such as a piece of writing Your essay's too long - it needs cutting down a little. cut sb down to size to make someone realize that they are not as important, successful etc as they think they are（《朗文当代英语词典》）