You won't be able clear the config to the running config because the ASA will be using the running configuration to all the connectivity, etc.
The best way to clear the config and to paste the new config would be through console access as you have done. This way, it will ensure that you do have connectivity to the ASA just in case there is any config error with the new config that you pasted to the ASA.
Alternatively, you can also copy the config to the start up config, and reload the ASA as ASA uses the start up configuration when it reloads. Upon reload, it will copy the start up config to the running config for the ASA to use. However, as advised earlier, there is risk in clearing all the config and pasting the brand new config remotely as there is a chance that some feature might fail due to misconfiguration (human error normally plays a part, typically not intentionally).
Hope that answers your question.