If you can't get a bigger cutting board, here are a couple pointers to getting the most done CLEANLY in a small space (mostly tricks from my kitchen manager):
Use a sharp knife.
It's easier to control, and when you chop, pieces don't move as much.
Hone it at least daily to keep the edge aligned.
Organize your work on the board.
If you're right-handed, keep raw ingredients on the left side, and finished, cut product on the other.
Keep the spot you're using to cut clear.
It may only be 4-6 square inches, but it shouldn't have anything to get in the way.
I like to use the bottom middle of the board for cutting and the corners & top to organize stuff in various stages of cutting.
Remove trash (trimmings, ends, unusable vegetable scraps) from the board.
Either keep a trashcan next to the counter, or use a bowl to collect garbage.
This frees up space on your cutting board.
You can use additional bowls to store uncut material, and finished results.
This frees up more cutting board area.
All of these tips help, but I'll tell you what my chef told me:
the bigger your cutting board, the more room you have to work, and the faster you can go.
As your knife skills improve, you will be able to work in a smaller space without problems.
But first, start off with plenty of room.
As you you gain experience, your cuts become more precise, you organize your space, and work faster and cleaner.
With this advice in mind, you should move to a larger cutting board.
The extra space to work make it much easier to develop proper knife skills, because you're not trying to cramp yourself in.
I suggest the largest board that you can comfortably fit in your sink for cleanup.
With professional knife skills, I can handle prepping multiple items on an 8.5" x 9.5" cutting board; however, I find that my 11" x 14" board provides a lot more room to organize my work, and is more comfortable to use.
At work, I use the biggest board I can fit on my station.
cooking.stackexchange.com/users/6345/BobMcGee
I disagree that your board is small.
My go-to everyday boards are about 4"x8" - smaller than a standard piece of office paper folded in half.
I use them to chop onions, carrots, cabbage, potatoes - even watermelon!
Sure, they're small.
But they fit easily in the dishwasher and the cupboard, and I have four of them
so I can always grab a clean one.
My tips: sharp knife.
We all agree on this prep bowl.
Don't accumulate finished product on the board - there's no room for it economy of movement.
Don't knock down neat piles.
Have a gesture repertory.
For example, when slicing a carrot I can do about 4-6" of carrot without moving the carrot.
Then one hand pushes all the carrot slices up towards the empty end of the board while the other moves the carrot forward
so I can start slicing again.
If the pile of slices wants too much of the board, it goes into a prep bowl.
I don't feel cramped at all cutting up one potato at a time or one of anything at a time and putting them into a pot or a prep bowl as I go.
I like that my cutting boards don't take over the universe when I am working.
I do own a giant wooden one which is mostly for serving pizza on, and occasionally for bread, a medium oval wooden one that gets a ton of bread use, and a giant plastic one that ...
well, if I recall correctly it mostly gets used by visitors who are more comfortable with large boards.
To me the advantages of the small boards are all I notice.
And I the meals I routinely cook serve 6-8 people.
cooking.stackexchange.com/users/304/Kate Gregory
It's probably mainly technique given that size, but you're working on the smallest board I'd consider suitable to the task without really cramping your style.
So much of knife work is the skills and technique - but its also the knives.
Dull, un-ergonomic knives really are a pain to use and the result is overall sloppy work.
All that said though - in cutting anything though, I always give myself as much space as I can.
Stuff falling off board and such starts to become dangerous(in a food safety concern), unless you just have a sparkling sterile kitchen.
If that's your biggest board, and you're cutting meat on it sometimes - I'd consider a bigger board for more reasons than an onion.
cooking.stackexchange.com/users/1374/rfusca
Use a very sharp knife and slow down.
A dull knife requires more pressure, and food (especially hard foods, like carrots) tends to break free and bounce around when you're cutting it up.
A sharper knife will allow you to use more of a slicing motion, rather than exerting pressure, and food will stay put better.
Working slower will let you concentrate on using a slicing motion rather than trying to push through the food.
It will also move the food around less, so you'll have less trouble knocking it off the board.
Also, keep a bowl nearby to transfer already-cut-up food into and get it out of your way.
cooking.stackexchange.com/users/5646/Adam Jaskiewicz
How do you get to Carnegie Hall?
Practice!....
To quickly improve your technique you may find a Mandoline Slicer helpful.
With the julienne attachment you can get strips quickly, easily and consistently.
Once you have the strips, dicing is easy and should be doable with a minimum of mess.
[The Mandoline slicer I provided a link to is a "typical model".
From Amazon to Walmart you may find a variety of brands and models with an assortment of attachments and of varying quality.
This is not an endorsement of a particular model.]
cooking.stackexchange.com/users/6279/Cos Callis
I have a fairly small cutting board - about 8.5" x 12.5" (22cm x 32cm), and I am finding it difficult to dice vegetables, especially the onions, without stuff going all over the place.  Is it my technique that's sloppy or should I just get a bigger cutting board?
How can I dice vegetables on a small cutting board?
cooking.stackexchange.com
<knife-skills><cutting-boards>
cooking.stackexchange.com/questions/17202
cooking.stackexchange.com/users/7147/Beyond Ramen
Transfer cut vegetables to a prep bowl and use a sharp knife to stop food from breaking free. A mandoline slicer may also be helpful. Transfer chopped vegetables to a bowl to leave space on your board. Make sure your knife is sharp.
Don't accumulate chopped vegetables on the board. Transfer them to a bowl. Use a sharp knife and don't try to work too fast. Try using a Mandoline slicer.