You want to clear the router's log buffer.
Use the clear logging command to clear the router's internal log buffer:
Router#clear logging Clear logging buffer [confirm] Router#
There are times when it is useful to be able to clear your router's internal buffer log. For instance, while debugging a network problem, old debug messages can cause unnecessary confusion during stressful moments. This will clear the router log:
Router#clear logging Clear logging buffer [confirm] Router>show logging Syslog logging: enabled (0 messages dropped, 0 messages rate-limited, 0 flushes, 0 overruns) Console logging: level debugging, 64201 messages logged Monitor logging: level debugging, 64820 messages logged Buffer logging: level debugging, 9 messages logged Logging Exception size (4096 bytes) Trap logging: level debugging, 2253 message lines logged Logging to 172.25.1.1, 2253 message lines logged Log Buffer (4096 bytes): Router>
Note that this command has no effect on the other forms of logging.