Some costs and poor investments will be straightforward to identify and cut, like the mediocre agency you've been trialing, the remarketing campaign that's not converting, or the software no one's using. But once all of the obvious cuts are made, you need to think bigger picture, rather than flinching at price tags, if you want your function to shine.
Underpinning the current execution of your marketing strategy you'll find investments with high returns, investments with mediocre returns, and zero-gain costs. When cutting spend, you want to concentrate on the latter two, but first, you need to find them. There are generally four buckets to assess: agencies, technology, people, and media spend.