The most common and most likely answer to this crossword clue is the 4 letter word CLIP
I've seen this crossword clue in Independent
C
L
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P
Buddy explains!

The straight part
We know that "Cut/speed" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case cut/speed = clip.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 CLIP mean?
CLIP noun- Something which clips or grasps; a device for attaching one object to another.
- An unspecified but normally understood as rapid speed or pace.
- An embrace.
- A frame containing a number of bullets which is intended to be inserted into the magazine of a firearm to allow for rapid reloading.
- A projecting flange on the upper edge of a horseshoe, turned up so as to embrace the lower part of the hoof; a toe clip or beak.
- A gaff or hook for landing the fish, as in salmon fishing.
- To grip tightly.
- To fasten with a clip.
- To hug, embrace.
- To collect signatures, generally with the use of a clipboard.
- Something which has been clipped from a larger whole:
- An act of clipping, such as a haircut.
- The condition of something, its state.
- A blow with the hand (often in the set phrase clip round the ear)
- To cut, especially with scissors or shears as opposed to a knife etc.
- To curtail; to cut short.
- To strike with the hand.
- To hit or strike, especially in passing.
- An illegal tackle: Throwing the body across the back of an opponent's leg or hitting him from the back below the waist while moving up from behind unless the opponent is a runner or the action is in close line play.
- To cut off a signal level at a certain maximum value.
- To discard (an occluded part of a model or scene) rather than waste resources on rendering it.
- (Of a camera, character model, etc.) To move (through or into) (a rendered object or barrier).
- To cheat, swindle, or fleece.
- To grab or take stealthily