Yes you can do this a couple different ways.
You can use the Export Area tool, whihc allows you to temporarily crop an area on the screen and then export that specific selection without affecting the overall design.
You can also right-click on the object and choose Insert Rectangular slice. Then apply the desired optimization settings to the slice. Then right click again on the slice and shoose Export Selected Slice. This option is a little more accurate than the first option, as Fireworks ensures that the slice covers the entire object.
Another option is to convert the object to a Button symbol, which allows you to add up to 4 states to that specific object. Once the symbol has been created, you can again choose to right-click and export selected slice.
Hope this helps.