With the AXvoice Call Blacklisting feature, you can blacklist calls from as many numbers as you want. Just add the number to the Blacklist from your AXvoice web account and you are done.
With AXvoice, you don't only get to mute the notifications (see: Do Not Disturb) but also the actual calls using your AXvoice VoIP. This way, you don't have to deal with the unwanted calls in any way.
No, your online AXvoice online account doesn't hold a record for the blocked calls.
You can blacklist a number by going to your AXvoice web account. To blacklist certain numbers, go to the "Features' page from your AXvoice online control panel and select “Incoming Call Features”. From there, click on the “Blacklist” tab which will take you to the “Blacklist” feature page. Enable this feature and start blacklisting numbers.