How to answer this without writing a book?
Let me get to the heart of the question first: Without knowing the details of the crime it is impossible to say if an expungement of a record will mean that there will be no deportation or inadmissibility or not.
But this can be said: Usually a conviction of a crime of "moral turpitude" leads to deportability and inadmissibility. That means, an alien convicted of such a crime cannot obtain a visa to enter the States or, if he already is in the States, is subject to deportation.
Now, the definition of "crime of moral turpitude" is the first stumbling block. What is this? The courts have so far included any sexual offense, most kind of thefts including even petite larceny, shoplifting etc, burglary, but also repeated driving while under the influence of alcohol.
Once it has been established that there is a crime of moral turpitude, then it needs to be established if there is a "conviction." This also has been the subject of many lawsuits. What is a "conviction" in the eyes of the immigration law? A short definition is: any final adjudication of guilt. Now this is also a jurists' term, but it really is too broad a topic to describe that here in detail. Let's make it short, if necessarily a little imprecise: it is only a conviction if a judge entered a judgement of guilt. If you were given probation with the possibility of dismissing the charges after the probationary period and similar things, it would not be seen as a "conviction" for immigration purposes.
Now, even if a conviction occurred, there is the matter of expungement. Does an expungement mean that you cannot me deported or kept outside the US? That, too, has been hotly contested in court. Today this can be said:
In most cases of crimes of moral turpitude the CIS policy is to accept an expungement as removing deportability or inadmissibility, in other words, if the record has been exponged, you will not be inadmissible or deportable because of that crime.
BUT, that still does not go for every case. Drug cases, aggravated felonies and similar crimes are being treated differently.
So you see, there are so many variables and exceptions to the rules that I recommend to consult an immigration attorney prior to any visa application or visa renewal if there was any criminal proceeding against you except for a clear cut dismissal of the charges.
If your case was dismissed you should not have any problems. But for peace of mind, check the details with an immigration attorney.
By the way, yes, Department of State Visa applications ask for "arrests" as well as for "convictions." Consular officers then will apply the rules I mentioned when you answer this question with "yes." An arrest that was not followed by criminal proceedings, though, will never lead to inadmissibility.
Last: What does expungement actually mean. Here I quote from a website:
When records of an arrest or conviction are sealed or expunged (a notation is made in the file that the records are off limits to all except law enforcement personnel), defendants can, for some purposes, treat the arrests or convictions as though they had never happened. For example, assume that a defendant's conviction for misdemeanor possession of an illegal drug is expunged. On applications for school, a job or a professional license, the defendant may be able to answer that the defendant has no arrests or convictions (assuming no others exist). However, the rules about who is eligible for expungement, and the effect of expungement, vary from state to state, and people interested in expungement should seek the advice of an experienced attorney.