The most common and most likely answer to this crossword clue is the 6 letter word AXEMEN
A
X
E
M
E
N
Buddy explains!

The straight part
We know that "ruthless cost-cutters" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case ruthless cost-cutters = axemen.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does AXEMEN mean?
AXEMEN noun- A man who wields an axe.
- A musician who plays a guitar or saxophone.