The only way you can get an assault charge expunged is if you have been found not guilty or the case has been dismissed. If you are found not guilty, then you can immediately get the record of arrest and the records of the charge expunged from your criminal record. That means that the records will be destroyed, deleted and erased and it would not show up on a background check and you could legally say that it never happened.
If you get deferred adjudication for assault, not on a family member, that can later be sealed from your record. The procedure for this is called a motion for non-disclosure. A judge can order that the record be sealed. It is limited and not available to the public. It is limited to just law enforcement, it is not disclosed to the public, it does not show up on a background check and you can legally say that it never happened.
The distinction is that law enforcement keeps a record of it and it can be used against you in the future if you ever get into trouble again. However, if it is an assault on a family member, even if you completed a deferred adjudication, you can never seal that from your record. So, there are different kinds of levels of ability for cleaning up your record on assault charges.