It is pretty much impossible to avoid the fact that every person will make mistakes at work at one point or another, and for the most part, the people with whom you work will be perfectly understanding when you make such mistakes (after all, it has probably not been all that long since they made a mistake at work themselves!). But of course, there is a difference between “making mistakes at work” and “making big mistakes at work”; big mistakes are no different from little mistakes in that they really can happen to anyone at any point, but big mistakes usually tend to be more costly, and it is for this reason that you will want to make sure you know how to avoid making big mistakes at work.
In order to eliminate bad mistakes at work, probably the best thing you can do is always double check your work; it is easy to get so comfortable in your job that you end up never looking back over the work you have done, but once you get in the habit of taking a few extra minutes to always double check your work, you will be able to catch all those little mistakes that happen, and more importantly, you will be able to catch those big mistakes when they come along!
Always being willing to ask questions and try to learn more is another way to avoid making big mistakes at work; it is easy to get comfortable in a job and assume that you already know all there is to know about it, but when you get in the habit of always trying to learn more, you will be able to continually improve at your job, which will continually separate you from those bad mistakes that can be made.
And realize that there will still be times at your job when things will go wrong, even when you do these things, and the manner in which you react to these things going wrong will be key; rather than simply getting upset because things went poorly, learn to always break down what went wrong, identifying the problem so you can avoid it next time around.