The most common and most likely answer to this crossword clue is the 9 letter word SANDPAPER
I've seen this crossword clue in Financial Times
S
A
N
D
P
A
P
E
R
More clues leading to the result SANDPAPER
- Abrasive guide appears around North Dakota
- Smoother and sounder without ultimate in bland drivel
- Breast feeding Polish queen becoming abrasive perhaps
- Student leader with essay that’s abrasive
- Abrasive doctor appears extremely narked
- Flyer’s first person booted out by aircrew, primarily for rough stuff
- Abrasive doctor appears to control new department
- It is rough, could be smoother
- Hospital doctor keeps soft copy smooth
- Son with a supporting father is abrasive
Buddy explains!

The straight part
We know that "that’s abrasive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case that’s abrasive = sandpaper.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 SANDPAPER mean?
SANDPAPER noun- A strong paper coated with sand, ground glass, or other abrasive material for smoothing and polishing.
- A sheet of such paper.
- To polish or grind (a surface) with or as if with sandpaper.