I'm running a .47 size motor with an 11x6 propeller. The problem with this is while on the ground I'm cutting up grass. I have less than 1" of clearance to the ground. What would you suggest?
A 10" propeller or going with larger wheels from 2 1/4 to 3ish or both?

I'd do larger wheels, 3 1/4 inch will give you what you need. 3 inch will also work. The 11X6 on a 46-47 size engine is about perfect

What airplane?
What kind of runway? Paved or grass? Tail dragger or trike?
I fly off a grass runway with 2-1/4 nose, 3" main trike gear.
I have a TT Pro .46 and it runs real well with an 11-7 prop.
If it is a trike gear and you upsize the nose wheel you should also upsize the main by the same amount.
If you go with a shorter prop make sure to use a higher pitch like 10-8 so you don't have your engine over rev.
Another option is a 3 blade prop. It can be shorter but still produce efficient thrust and load on your motor.
One more edit: no matter what changes you make it is a good idea to check your balance again.

The 3-bladed prop is a nice solution that is often overlooked. A 10x6 3-bladed prop will provide the same thrust as an 11x6 2-bladed prop, but it will likely be much more quiet. I upgraded my Tiger Stick to a 3-bladed prop when I put a Magnum .52A XLS 2-stroke on it to provide extra load without shortening the ground clearance. The plane is super fast, reasonably quiet, and still shoots across a grass field without throwing off clippings.

The bigger wheels not only help with prop clearance, but they will allow the airframe to roll much more smoothly over grass.

Both upgrades are handy for flying from grass fields.

Another idea, depending on how hard, is to build you some custom landing gear or get some new that will give you more ground clearance.

The plane is a Nexstar. I haven't taken it to the field yet. I've just run it around the backyard with the wing off. That way I won't be tempted in taking off . We are in our 3rd week of rain. I got a call today from the person that takes care of the field and it won't be dry enough for a couple of more weeks. I'll try the 3" wheels first. Putting on a 3 blade prop also sounds interesting. Because this thing is real loud. After cutting the grass I decided to take it out for a spin. Nobody would even hear the engine over the sound of all the weedeaters running. It sounded like a weedwaker on steroids. Hopefully you guys have better weather. I think I heard the weatherman say 3 to 4 more days of days in the forcast.

If its a nose wheel, put a big 3" on the front to lift it up a bit. Since its a nextstar with their "fancy" landing gear, ignore my previous statement.

Don't just lift the nose. If you are going to replace the wheels (which I would suggest, especially since you suggest that you are flying off of grass), replace them all with some 3 1/4 inchers. They will roll much easier over the grass. Lifting just the nose of the plane will give you fits trying to keep it straight on the runway--basically nullifying all that is benificial about a trike setup. P-factor will come back into play, and the plane will be a bit squirly on the runway. Just lift the whole thing up and you will be fine. Also, think about the 3 bladed prop. I've had to do this with twins (because of clearance from the nacelles to the fuse), and also on a sea plane that I'm currently building (because of clearance from the engine pod to the fuse). Three blade props really are nice! And, as an added plus, it will help you slow the plane down for landings much easier!

Go with larger wheels. My experience has shown that MOST 46 size planes need 3" - 3 1/4" wheels to fly from a grass field. Make sure you replace ALL THE WHEELS, not just the nose wheel on your nexstar. Replacing just the nose wheel will make the plane take off before it has adequate airspeed to fly.

As for the 3 blade prop - If you ABSOLUTELY NEED IT fine, however, 3 blade props are not only more expensive than a 2 blade prop, but they are less efficient than a 2 blade. I have used a 3 blade on a couple of occasions - on one occasion I had insufficient ground clearance and redoing retracts was not an option, the other occasion was for a scale appearance. In the second case the prop was replaced after one flight with a 2 blade prop (3 blade 10x6 -> 2 blade 11x6 ). The difference in performance was like night and day.

Ditto the 3-1/4 inch wheels. They are a necessity at our field. Our grass is always on the long side.

I think I'll start with the 3" wheels as suggested and see how that goes.
If this doesn't do it, I'll give the 3 blade prop a try.