|set remindersOpen to application "Reminders" is running|
|set monthAgo to (current date) - (30 * days)|
|tell application "Reminders"|
|set myLists to name of every list|
|repeat with thisList in myLists|
|tell list thisList|
|delete (every reminder whose completion date is less than monthAgo)|
|if not remindersOpen then quit|
Copy/paste the script into the "Script Editor" application (Applications -> Utilities), press play.
Or you could save this to a file, "Purge Old Reminders.scpt," and then from Terminal use the command line program osascript,
You'll be asked to grant Terminal permission to access your Reminders.