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This is an impressive tool and I am planning to use it in a class this semester. My problem is that they are just starting to do Boolean logic, truth tables, maps, and circuits. So, while I want them to be able to draw their diagrams, I don't them to be able to use the analyze circuit functionality just yet. They need a little more background before they should use a tool like that.
Is there a good way to limit the program's functionality?
I'd be interested in what other instructors have to say. I don't mention the feature to my students, and by and large they don't find it on their own. Some have - but my experience has been that it's pretty obvious when students try to build a circuit automatically: The circuits thus built tend to be extremely large. In fact, I write the assignments saying that students will be penalized for using far too many gates, and I choose problems where the sum-of-products approach results in a huge circuit. I also write them where the number of inputs is large enough that it's easier to just build the circuit than to fill in the truth table.
The other example that I know of somebody dealing with this is at Berkeley, where their project description mentions the Combinational Analysis feature. It says something like, "We don't forbid using this feature, as that would be impractical. But we definitely advise that you avoid it, since it won't be available to you on your exams."
But to answer your question directly, there isn't a built-in way to limit the program's functionality like this. One basic approach, though, is to modify the distributed JAR to remove com/cburch/logisim/analyze/gui/Analyzer.class. This is the file implementing the Combinational Analysis window - so any attempt to load it would fail on an exception. But students will be able to find the non-hobbled version easily, so I don't really see much point in that.
If none of this sounds good, you could start the students out on a much simpler system. I like the Java applet http://math.hws.edu/TMCM/java/xLogicCircuits/ but there are lots of simple alternatives to Logisim out there. Their feature sets are usually rather small - actually, come to think of it, I haven't noticed any with a feature approximating Combinational Analysis in Logisim (though some also have features that Logisim lacks).