Southstar,
Home Depot primarily only carries sandpaper for working on wood with. I frequent Home Depot and Lowes pretty regularly. I generally only see up to 400.
In any event, 600 isn't that smooth compared to most knife sharpening media.
600 "WILL" sharpen though and 400 - 600 are pretty decent grits for still cutting steel at a noticable rate, but they tend to leave a toothy edge.
To get a quality, fine, polished, shaving, push-cutting edge, you will need to go to finer grits.
For sandpaper finer than 400 (finer than 600 in your case), you will need to go to an "Auto" parts store. Most auto-parts stores carry 800, 1000, 1200, 1500, 2000 and sometimes 2500 grit sandpaper.
I have tried these fine sandpapers and they do work, but quite honestly, they are NOT worth the cost. IMO, sandpaper starts loosing it's value at about 600 - 800 grit.
The problem with the high/fine grit sandpapers is that they cost a LOT more than the sandpaper you can buy at Home Depot and you get smaller sheets for the higher cost = a LOT higher cost.
But, it gets worse, the grits on the finer sandpaper don't even last as long as the coarser grit sandpapers - so, you also get less wear/usage/mileage out of the finer grit sandpapers.
In the end, it is WAY worth doing just a bit of research and planning to buy or make yourself a leather strop and use the "compounds" for abrasives instead of the fine grit sandpapers.
The compound abrasives cost a bit more up-front, but they last WAY longer than sandpaper and quickly start adding up to significant savings.
Also, IMO, the compounds on leather actually work better and more of a joy to use.
One other minor little bonus, the compounds are wax based and help hold some of the grind residue. While both make their own sort of mess, I find the compounds a LOT less messy. I often like to strop in my den while in front of the TV. I actually recommend watching your knife when stropping, but I find I can sort of do both. When I have used sandpaper, I spread out newspaper on a little folding table or similar and still end up with a big "Dusty" mess. The strop still makes a smaller mess, but mainly not nearly as dusty.
Buying a leather strop is not real expensive, but it is an investment that should last for MANY years. And if you don't want to pay $25 - $40 for pre-made strop, you can make your own out of very inexpensive materials. Making a leather strop is as simple as cutting to shape and gluing a decent piece of leather onto a board. All you have to do is decide what size and shape strop you want and where to find a decent piece of leather for a strop.
Some choppers need a bit of sanding to true some dents and rolls. But, once most knives have a good edge, they tend to just need a few quick passes on a leather strop to stay shaving sharp.
Anyway,.... I have written and rambled enough about this in the past:
Sharpening Thread .