The most common and most likely answer to this crossword clue is the 4 letter word OOZE
I've seen this crossword clue in The Daily Telegraph
O
O
Z
E
Buddy explains!

The straight part
We know that "slimy stuff" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case slimy stuff = ooze.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 OOZE mean?
OOZE noun- Tanning liquor, an aqueous extract of vegetable matter (tanbark, sumac, etc.) in a tanning vat used to tan leather.
- An oozing, gentle flowing, or seepage, as of water through sand or earth.
- Secretion, humour.
- Juice, sap.
- To be secreted or slowly leak.
- To give off a strong sense of (something); to exude.
- Soft mud, slime, or shells especially in the bed of a river or estuary.
- A pelagic marine sediment containing a significant amount of the microscopic remains of either calcareous or siliceous planktonic debris organisms.
- A piece of soft, wet, pliable ground.