Try WEvtUtil.exe
There's no way via the GUI to clear all logs at once. At least not that I've ever found. :)
Loop and delete with intermediate file
Here's a batch file that uses WEVTUTIL.exe to list the logs into a text file, and then use that text file to delete each of the logs.
WEVTUTIL EL > .\LOGLIST.TXT
for /f %%a in ( .\LOGLIST.TXT ) do WEVTUTIL CL "%%a"
del .\LOGLIST.TXT
timeout 30
If you feel unsafe having this all in one batch file, then you can save this to two separate files and then run one after the other:
(The "Nuke" batch will just error out if it doesn't find a "loglist.txt" in its current directory.)
Populate-LogList.cmd
@ECHO OFF
REM Source: https://superuser.com/a/655185/389368
WEvtUtil.exe enum-logs > .\LOGLIST.TXT
Nuke-LogList.cmd
@ECHO OFF
REM Source: https://superuser.com/a/655185/389368
for /f %%a in ( .\LOGLIST.TXT ) do WEvtUtil.exe clear-log "%%a"
del .\LOGLIST.TXT
timeout 30
Loop and delete directly
As Logman pointed out in his answer, this can be further shortened down (and eliminate the need for the intermediate text file) by using something like (%'s double for batch file):
for /f %%a in ('WEVTUTIL EL') do WEVTUTIL CL "%%a"
timeout 30
Run as Admin!
Whichever way you choose, ensure you "Run As Administrator".
Easiest solution I've found. Been using it since Vista. :)