I do this in my testing framework so that each test has its own HAR file for debugging purposes. Even when they use the same browser.
The command you are looking for is "new_har". This creates a new session and begins logging to a new HAR file. You can also specify a name for the session. I normally get the old HAR first and save it before clearing and starting a new session. But you don't have to do that if all you want to do is clear the proxy log.
Here is an example using the Python module.
from browsermobproxy import Server
server = Server("path/to/browsermob-proxy")
server.start()
proxy = server.create_proxy()
from selenium import webdriver
profile = webdriver.FirefoxProfile()
profile.set_proxy(proxy.selenium_proxy())
driver = webdriver.Firefox(firefox_profile=profile)
proxy.new_har("google") # Start first session
driver.get("http://www.google.co.uk")
proxy.har # returns a HAR JSON blob for first session
proxy.new_har("Yahoo") # Start second session
driver.get("http://www.yahoo.co.uk")
proxy.har # returns a HAR JSON blob for second session
server.stop()
driver.quit()