By the Margulis superrigidity theorem, any homomorphism from $SL(n,\mathbb{Z})$ to $SL(n-1,\mathbb{R})$ with infinite image has to extend to a homomorphism from $SL(n,\mathbb{R})$ to $SL(n-1,\mathbb{R})$. But any non-trivial representation of $SL(n,R)$ has to have dimension at least $n$, so this is impossible.
The best online source for the Margulis superrigidity theorem is Dave Witte Morris's unfinished book
http://people.uleth.ca/~dave.morris/books/IntroArithGroups.html
The above argument uses Theorem 12.1 and Theorem 12.3.
