4 mm any stage is this serious bone cancer?

Cancer Staging: Every variety of cancer has a unique ajcc staging system, known as the "tmn" system. The "t" part includes the size of the primary tumor. You did not specify whether you meant a primary tumor, such as breast, colon, or lung, that has metastasized to a bone, or you really meant a primary bone tumor. If the former, the cancer is a stage 4 lesion - serious. If the latter, it depends. Need more info.

Yes: Generally, all bone cancers are serious regardless of the size. However, some are more aggressive than others it really depends on the actual subtype of bone cancer and what it looks like under the microscope. That being said, most bone tumors that are truly cancerous are bigger than 4mms.