Unfortunately not. 'Rosetta' allowed some PowerPC apps to run on Intel based Macs until 10.7 (Lion). On 10.8, however, Rosetta is gone and so have the PowerPC apps that used to run because of Rosetta. There is no way you can get Rosetta back onto 10.8 to emulate PowerPC apps.
Dreamweaver MX is a pure PowerPC app and is not compatible with Universal Binary - which is what 10.8 works on.
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As Sudarshan states, because your operating system doesn't have the "middleware" that translates Power PC code into Intel-processor code, Dreamweaver MX is not going to run. But Rosetta support ended with Snow Leopard, not with Lion. Apple did tell everyone that they would not support the Power PC platform forever back in 2000, so everyone was encouraged to move their code forward.
Adobe did that and their new products support Intel.
Look through your applications in your /Applications folder. Do a "Get Info" on them (click on their icon and press [command]-I or right-click on the icon and select Get Info.
Under General, you'll see what kind of application it is and there are three types:
- Intel - won't run on a Power PC, will only run on the newer Intel Macs.
- Universal - will run on either an Intel or Power PC computers.
- Power PC - Will not run on Intel Macs unless you have Rosetta.
In the case of Dreamweaver MX, I think you'll see that it's Power PC. And, if I had either an old Mac Mini (Power PC G4) or an older Mac that I did not want to upgrade past Snow Leopard, I'd run it on that machine, as it enables you to insert inline code and style stuff without using a stylesheet, which can be very handy for creating HTML email messages.
I currently have Dreamweaver CS3 (Universal) on my Mac Pro, running Snow Leopard. I also have Dreamweaver CS 5.5. The advantages of 5.5 over 3 are numerous, the first of which is the "Live View" and "Live Code" modes, where Dreamweaver actually becomes a Webkit Browser and shows you really what your web page will look like. (Live Code uses your testing server and that lets you run server-side code in a test, Live View gives you a very quick look-see for static pages without the need to preview in a browser).
So, to keep building your website, buy the current version of Dreamweaver or downgrade your Mac's operating system to Snow Leopard or below.