I submitted a manuscript as a Research Paper last May 12 to Journal A. Now, 6 months later, I have received a decision letter recommending "... undertake a major revision, and re-submit a revised version of your paper as a Technical Note". Talking with co-authors we disagree and would like to submit the paper to a different journal (Journal B). What should I do? Should we submit the paper to Journal B if it is still "under revision" in Journal A? I have sent a letter to the Editor of Journal A, explaining that we'll not re-submit the paper as a technical note, but I have not yet received any reply. Thanks for the advice!
To make it clear to the editor, formally withdraw it from consideration. Then it is yours to do with as you please. They have no hold over you or the paper until you formally sign copyright away. What you have sent is likely enough, actually, but a formal notice of withdrawal leaves no ambiguity.
In most places I think that giving notice is enough and their reply isn't needed. But you need to keep records. Formal mail (sneaker net) with a receipt for delivery is sometimes used for such things. And keep the receipt.
I have sent a letter to the Editor of Journal A, explaining that we'll not re-submit the paper as a technical note
I would consider this to be withdrawing your submission, assuming the explanation did not include any request to reconsider your paper in another form. You can now submit it someplace else, it's not necessary to wait for your withdrawal to be acknowledged or for the software to change your status from "under revision". There is no work the journal is currently doing on your paper, they are just waiting for you - it would be very different if it were out with reviewers.
However, if you haven't already revised your paper based on the comments you received I would highly recommend doing so before you submit someplace else. Even if you disagree with the reviewers' suggestions there must be something useful you can extract from them to clarify and improve your manuscript.
If you do submit it someplace else, and afterwards the original editor comes back and changes their mind and says you could resubmit as a Research Paper (I think this is incredibly unlikely, just including this to be thorough) you will have to politely tell them that you intended to withdraw the submission and have already resubmitted elsewhere.