I would take close up images of the tile so you don't see the edges, only the texture and colour in the same way as they do with carpet and wallpaper. You don't need to see the tile edge unless its a set, but then i would just lay them out in a set and take a photograph in the same way.
Maybe do that with even non set tiles, lay them out as they would be on a wall and try different white balance settings and lamp positions to get the effect you are looking for.
If you want to set up your own mini studio, use a huge piece of card preferably brilliant white. If you can bend it (don't let it crease), it will be exactly how we do it in a studio with much more expensive equipment but basically the same principle. Bend it so you when you position the camera you cant see the edges of the card, then position the object in the curve of the card. Position the lights so that they don't glare at the object. I usually bend a piece of paper over the front of the lamp which gives it the diffuser effect that the pro lamps use. Just use any bed side or desk lamp but just be careful of the heat on the paper. Try and bend the paper as far away from the bulb as possible to avoid the heat, just make sure you turn them off when ever you walk away from the setup.
You can see these objects I photographed
http://www.quicktimevirtualreality.com/objects.html
The Flash gun and Engine component were photographed on my dining room table. If you have Quick Time installed you can see a virtual reality movie with all the images i took.
Don't look into blue screens or any other colour backgrounds as you get some thing called "radiosity", which is when the colour of the background actually reflects onto the object and then discolours the object that colour, which is more difficult to remove (without a lot of talent and good software) than if you just used a simple white background in the first place.
After all that above, you wont need to cut them out, as the image will be right first time

)
Hope this helps
Ian