There are often two parts to a question like this:
Could you say it; and
Would you say it?
And, often the answers to these questions are not the same.
The wise man who knows justice
Clearly this describes some specific characteristics of a person – they are both wise and just. To say that someone knows justice is suggestive of something that combines both knowledge and understanding:
To have knowledge or information concerning (something), esp. as a consequence of observation, inquiry, or study; to have ascertained, learned, or found out; to have a correct idea or understanding of. - OED Online
The second part is more open to opinion and depends upon the meaning that you want to convey
…can stop quarrelling or argument.
I’m going to disagree others replying here and say that, grammatically and semantically, this is acceptable. Quarrelling is straightforward but Argument is more complicated. The safest way to go is, as has been pointed out is to match …ing with …ing. So, quarrelling and arguing is fine. You could also go with plurals – quarrels or arguments Argument though can also mean a process rather a single instance or multiple instances and, if that’s the case here than it can be used. Think – quarrelling and conflict or quarrelling and strife.
I’d also warn (or argue) that Argument may not be the right word in the first place. Quarrelling has a clear negative meaning, it’s rarely used in a way that suggests a positive outcome. That’s not the case with argument and, as a result, your wise and just man may be in favour of it.
If we agree that you can say it then the, very valid, second part of the question is, would you? Is it ‘natural’ English?
The answer here is, not really. It sounds a bit like the translation of a Confucian proverb – deep, wise and philosophically sound, but not the kind of thing that you’d drop into normal conversation.
For a start – quarrelling and arguing: there’s a huge overlap there, while that is a valid rhetorical device it can sound clumsy like running and sprinting or, for that matter, speaking and rhetoric
It sounds to me that the message that you trying to get across is that:
A wise and just man can stop quarrels
However… The original version would make an awesome fortune cookie.