For what GP mentioned ("systems automation") depending on the JVM (as one would with Clojure) is kind of a non-starter, due to the long startup time. By contrast, Clojurescript (essentially the same language, but compiled to JS instead of JVM bytecode) can run in something like Node.js, where startup times are considerably faster.
Edit: this new development (CLJS compiled with CLJS) is remarkable because previously, compiling CLJS required a running JVM. One could still compile automation scripts and run those, but that wouldn't really be true to the "scripting" style anymore.
You can dynamically compile and run ClojureScript scripts so long as you have properly hooked things up to a JavaScript engine. I've started on an effort that makes this easy OS X, wrapping JavaScriptCore and I could see similar efforts for Node.js. Here's what I've been working on: http://planck.fikesfarm.com It can run scripts you have on disk, etc, and it has basic file I/O capabilities at the moment so you can write simple text processing scripts, for example.
Just for DX / ergonomics, I'd like to mimic more of the file I/O stuff that you have in Clojure, especially the ability to cope with streams. And then perhaps having network I/O would be interesting as well.
Then there is the `clojure.java.shell` namespace that could prove very useful for scripting.
Since none of your other responders said this, I will also point out the most common/obvious reason: you're building a website in Clojure, and want to continue using it for your front-end work, too.
Edit: this new development (CLJS compiled with CLJS) is remarkable because previously, compiling CLJS required a running JVM. One could still compile automation scripts and run those, but that wouldn't really be true to the "scripting" style anymore.