The most common and most likely answer to this crossword clue is the 10 letter word SCURRILOUS
I've seen this crossword clue in The Guardian
S
C
U
R
R
I
L
O
U
S
More clues leading to the result SCURRILOUS
- Foul slurs wrongly associated with curio
- Offensive son, eager to learn about right, left separately
- Vulgar and expensive car with ludicrously luscious upholstery
- Abusive rascal interrupting Hindu’s address, endlessly base person
- I scour URLs, which could be interpreted as defamatory
- Vulgar rascal — immature lout — to get small punishment aboard ship
- Slur, curious, distorted, defamatory
Buddy explains!

The straight part
We know that "Offensive" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case offensive = scurrilous.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 SCURRILOUS mean?
SCURRILOUS adjective- (of a person) Given to vulgar verbal abuse; foul-mouthed.
- (of language) Coarse, vulgar, abusive, or slanderous.
- Gross, vulgar and evil.