Unfortunately, no. The only way to get a good polish on your stone is with fine diamond powder on a lapidary wheel.
You can make your own home-made "lapidary wheel", but it won't give you very good results. (In Burma, the locals facet by putting the rough stone on a dopstick and scraping it at the appropriate angles on a block of metal that has diamond powder on it. The result is a faceted stone, but with very poor polish and dimensions.)
Some commercial Topaz is coated to give it a funky rainbow look, or more vibrant shades like pink & green. As "Neptune" Topaz is a trade name that I'm not familiar with, I'm not sure if your stone has been coated. If it is, don't try to re-polish it as it will lose its color.
The best thing to do is to go to a jeweller to see how you can salvage it. Sometimes, the cost of repolishing a stone may be more than the cost of replacing it!
*** Oh, so it is a Mystic Topaz! Those are cute little stones aren't they?! Most Mystic Topaz are coated on the pavilion, so you may be able to re-polish it without losing the rainbow effect or the color. However, some are coated on the table or on the whole stone. Repolishing such stones will drastically affect their appearance! My advice is - don't bother re-polishing it. It'll probably be cheaper to get it replaced.
Me - I'm a gemologist and I took a crash course in lapidary arts last year.