This is a very common problem, and the solution lies in psychology. You need to approach your timed problems with the same thoughtful calm you are able to apply in your untimed review. How do you do that? Well, you start by committing to do it!

Don't tell yourself "Oh no! The clock is ticking!" Instead, picture yourself as a very wise person seated on your meditation mat, perhaps sipping a warm cup of green tea. Ask yourself "What is this problem asking for? What do I know about this?" Occasionally, the answer will be "I have no idea!" to the first or "Nothing!" to the second. Those are the problems on which you guess and move on. However, most of the time you probably do have an idea of what is going on; you just need to approach the problem calmly enough to apply this knowledge.
A few general principles to make this work:
1) A little up-front work can save you a lot of time and trouble.
Most people are too quick to rush into the task--manipulating equations, testing answer choices or DS statements, etc. Take some time at the beginning to really understand what's going on in the problem. Rephrase the question if possible, especially in DS. Also, create a solution expression if possible. For instance, if the answer to the question will come in the form of a fraction, identify what the fraction should have in it, like this:
Women/Total = W/(M+W) =
2) Don't get stuck!
If you find yourself staring or rereading without comprehension, do something to break yourself out of it. Take a micro-break (just a few seconds to breathe calmly with your eyes closed and your body relaxed), focus on the actual question part to see what the problem is asking for, or create a chart or table to organize the information.
3) Use your scratch paper effectively.
Some people pride themselves on their ability to work problems in their heads. However, most people do not have this talent, and even if you do, you are still probably more effective with a little support from your scratch paper. As a GMAT instructor, I can do most GMAT quant problems quickly in my head. However, when I am really taking the test, I'm not seeing *most* GMAT problems--I'm seeing problems at my difficulty level, and that's true for everyone who takes the test. When we're being tested at our level, we need some support to avoid making little errors. Here are a few good uses for your scratch paper:
*Organize your variables and what they stand for (along with values if you're using Smart Numbers).
*Clearly mark what the problem is asking for and fill that in before choosing your answer.
*Track important constraints (x =
even integer; n =
perfect square)
*Create charts/tables to organize your work on many problem types (rates, before/after, multiple ratios, etc.)
*Write out explicit steps of your work. This doesn't necessarily mean writing
everything down. It just means writing enough to reduce your error rate to a more acceptable level. (We don't ever need to be 100% error-free!)
4) Review thoroughly
before checking your answers.
Most people check their answers immediately and spend most of their energy reviewing the problems they missed. This is actually not a very effective way to study! You should leave lots of time in your study schedule to engage in untimed review of every problem. Decide for yourself if you got it right or wrong, if you approached the problem effectively, and what you can learn about the test and yourself from this problem.
Then check the answers and review again as needed.
I hope these guidelines help. The anxiety you feel under timed conditions may never go away entirely, but that's okay--a little anxiety can be repurposed to increase your focus. However, you should start to feel calmer as you master more material, grow accustomed to the timed experience, and learn the techniques that work best to keep you on track.
Happy studying!