What is the procedure with regard to unfinished thesis if I am terminated from the program?
Departments generally do not terminate PhD students without letting the student's advisor know in advance. The fact that your advisor has not responded to you for 3 weeks, suggests the possibility that he/she is ignoring you. This is reasonable behaviour, if in fact your advisor was behind your termination.
As you are not currently in the US, you need to call your department chair and/or the chair of graduate studies and figure out what is going on. In my opinion, it is too soon to look for a new program or to start really worrying about your data.
In general, I've never heard of a student who was dismissed from a PhD program without sufficient warning and advance notice to make necessary alternate arrangements (for instance, write up and leave with a terminal master's instead of a PhD). The fact that you've been summarily terminated from a PhD program comes as a complete shock to me—you should have been given some knowledge and warning that this was coming.
However, the silence from your advisor is quite unusual. Even if your advisor were not supposed to converse with you about your situation, a short email saying "You need to address all of your concerns to [person X]" would not violate any such issues. So, it's not clear why your advisor is ignoring you—but it does seem rather obvious that your advisor has consented to your termination. (In my experience, if the advisor is willing to fight for a student, then only very serious issues such as plagiarism or sabotage will lead to termination.)
Out of curiosity, can you explain the significance of the article submission deadline? I finished my PhD in the life sciences, years ago. Having peer-reviewed publications certainly helped me complete in a reasonable amount of time, but the ‘deadlines’ to have these submitted were not true deadlines, but moving ones I decided upon with my advisor to push our projects along. I’m certain I missed more than a few of these.
In any case, my guess would be that your advisor is solely responsible for having you terminated for what they deem as lack of progress, and is presenting this as a decision made by the department. I’d agree with the others that this does seem very childish on their part, and if the only criticism they have is that you missed a paper submission, then you definitely deserve more of an explanation that that. I'm not sure exactly what your options are - but if I were you I would first want to know why I'd been terminated, and I wouldn't be satisfied with the reason you've been given.