Do you really need to use Excel itself? The issue here isn't so much that Excel doesn't work with Mono as that Excel doesn't work with Linux. You might be able to do something hacky with Wine in order to run Excel and the related COM interop on Linux, but I would probably suggest forgoing Excel altogether if you're going to use Linux. There are several libraries for manipulating .xls and .xlsx files in a more cross-platform way: an entire StackOverflow question is devoted to working with Excel files without using Excel interop.
Now, if you are doing more than simply creating files - for instance, if you want to use Excel's compute engine - then you probably have to use Excel itself. In that case, I see three clear options: (a) run Excel (and possibly your app as well) under Wine, and hope it works, (b) use Excel for Mac and run your server off of OS X, or (c) use Windows. I don't know if options (a) and (b) will allow proper COM interop, although I would expect that Wine tries to replicate all of COM and Office for Mac has some kind of API that takes the place of COM interop. The third option could come in two flavors: you could use Windows Server to run your website, or you could devote one machine or VM to the Excel calculation engine and contact that from the other parts of your web server code.