This kind of communication break down can be pretty detrimental to a relationship, so you're 100% right to look for help with it.
My ex and I had a similar style of communication breakdown. Half the time, using phrasings from the area we live in currently, he would be off in the completely wrong direction with what I said.
This, of course, was incredibly frustrating. Here's what we did to work on it:
Write things out.
When we had issues with very important discussions, we would step away and he would write out what he was trying to say. After he read over it to make sure it made sense, he would bring me this "letter" and let me read it with him in the room. This had two benefits, to my mind: First, I could not mishear him and he could not butcher his speech. What he was saying was clear and accurate. Second, if he still used phrasings that made no sense to me, I could ask him about it while he was sitting there without it getting in the way of my trying to read his core message. I feel like this facilitated more open and understandable communication, for both of us.
Explain what you hear when someone says "x."
Much like Rainbacon's answer, we went back after the incident and clarified things. For example, there were several occasions where my ex would go off on a completely different topic without giving me any indication he was discussing something different. Meanwhile, I was still discussing the original topic. Frustration ensued, and arguements were had. Until I started pointing out, after realizing he was on a different topic, that he hadn't transitioned the conversation in any way. Likewise, if I did or said something that threw him off or made me difficult to understand, he explained what it was and how it came across. Unlike Rainbacon's answer, we tried to do this as soon as it happened so long as we were not in a heated argument yet.
Walk away, return when you're both calmer.
It sounds like you're already trying this to an extent, but I include it for completion. Whenever we had any sort of misunderstanding or disagreement that came to an argument, one of us walked away and separated ourselves from the heat and anger. This allows us both to take a breath, cool off, and analyze what just happened. However, I had to make this strategy clear when I first started dating him. The first time we argued, I explained that I was going to step away and calm down, then we could discuss things rationally when we were both calmer and tensions weren't so high. Half the time, the follow up started with an apology from one of us. The other half of the time, we just brought a better willingness to listen and understand.
Naturally, these won't work for everyone or every situation. However, they are a good starting point to rebuilding your communication.
Personally, in your case, I would start with a conversation about communication. Sit down with your wife, and start similar to this:
Sweetheart, I've noticed in the past that when I say something, my meaning isn't always as clear to you as it was to me. My lack of clarity has caused at least a couple arguments or hurt feelings, and the last thing I want to do is hurt you with something I say. Can you help me understand where I went wrong with a few things?
This has a few benefits. It starts off by not blaming her, instead placing the fault on yourself. This will show a willingness to negotiate and not just blame her for the problems, which might also help a bit with communication between you. At the same time, you lay out the problem clearly and request her help to understand what she understood and how to avoid these kinds of misunderstandings in the future. Depending on if you keep the "last thing I want to do" part or not, you also reinforce that you care about her and how she feels, which never hurts in a relationship. (Well, as long as you mean it. I think you do, or you wouldn't be asking this!)
However you decide to work on this, include your wife. Make sure she's part of the solution. Communication is a two way street, and if you suddenly start communicating differently without bringing her in on things... It may worry or upset her more than just not getting your point/thought across.