A client created and activated a new milestone when I was finishing work on a previous project (contract with this client). This new milestone was not scheduled in advance and was not agreed with me. The fact is that at the moment, for family reasons, I do not have ability to fully work on a project on this milestone. I wrote about these circumstances to the client on the same day the new milestone was activated and asked to cancel the milestone. The client did not respond. I wrote to the client again, but the client did not respond. The client does not respond to my messages for 10 days (the client did not warn me that he would not be able to reply to messages, and I do not know when he will get in touch).
What can be done in such a situation, what variants can there be?
It sounds like you have already told the client via Upwork messaging and however else you communicate with the client that you cannot complete the milestone he created without your prior knowledge.
Whether he responds to you or not doesn't matter. You have notified him and any third party (such as Upwork) can easily confirm you didn't agree to the new milestone and have no intention of working on it.
If you expect you'll want to take on project at some future time, tell your client what that timeframe is and ask him to set up a new project/new milestone for that timing.
Thank you for the answer.
Assuming that the client will get in touch soon, some time ago I suggested to the client that I would make the introductory part of the project (this is a very short part). I made this part and asked the client to pass on the rest of the project to perform to another freelancer (the client did not respond).
What can I do to make this milestone canceled?
re: "What can I do to make this milestone canceled?"
You actually have the ability to close the contract yourself, without needing Upwork's or the client's help.
When you do so, you will be asked to refund any money funded in escrow, and that money will automatically go back to the client.
Alternatively, it is possible for the client to close the contract and request escrow money be refunded back to you. That will cause a refund request to be sent to you, which you may grant.