This is a little dirty Windows Powershell script which exports or backups Windows Eventlogs. The script creates a .evt file which can be used with the Windows Eventlog Viewer.

# Config
$logFileName = "Application" # Add Name of the Logfile (System, Application, etc)
$path = "C:\temp\" # Add Path, needs to end with a backsplash

# do not edit
$exportFileName = $logFileName + (get-date -f yyyyMMdd) + ".evt"
$logFile = Get-WmiObject Win32_NTEventlogFile | Where-Object {$_.logfilename -eq $logFileName}
$logFile.backupeventlog($path + $exportFileName)

And with the next code it cleans up older exported Eventlogs.

# Deletes all .evt logfiles in $path
# Be careful, this script removes all files with the extension .evt not just the selfcreated logfiles
$Daysback = "-7"

$CurrentDate = Get-Date
$DatetoDelete = $CurrentDate.AddDays($Daysback)
Get-ChildItem $Path | Where-Object { ($_.LastWriteTime -lt $DatetoDelete) -and ($_.Extension -eq ".evt") } | Remove-Item

UPDATE: If you wanna clean the Eventlog after the export you can do that by using the Clear-Eventlog cmdlet. (Thanks to Michel from server-talk.eu)

Clear-Eventlog -LogName $logFileName

And here the whole “script”

# Config
$logFileName = "Application" # Add Name of the Logfile (System, Application, etc)
$path = "C:\temp\" # Add Path, needs to end with a backsplash

# do not edit
$exportFileName = $logFileName + (get-date -f yyyyMMdd) + ".evt"
$logFile = Get-WmiObject Win32_NTEventlogFile | Where-Object {$_.logfilename -eq $logFileName}
$logFile.backupeventlog($path + $exportFileName)

# Deletes all .evt logfiles in $path
# Be careful, this script removes all files with the extension .evt not just the selfcreated logfiles
$Daysback = "-7"

$CurrentDate = Get-Date
$DatetoDelete = $CurrentDate.AddDays($Daysback)
Get-ChildItem $Path | Where-Object { ($_.LastWriteTime -lt $DatetoDelete) -and ($_.Extension -eq ".evt") } | Remove-Item
Clear-Eventlog -LogName $logFileName