Check the No Valid Address box on the Bio1 tab of the constituent's record to exclude that person from any mailings and reports (even if he or she does have addresses present).
There is an option on some reports and mailing functions to include constituents with No Valid Address so that they can be reported on.

For information on how the address is processed refer to How does marking Constituent has no valid addresses affect the Send mail to this address option on the address record?