With petit juries, (which is what non-grand juries are called), there is a process called "voir dire" during which both sides can remove prospective jurors in two ways: they can challenge prospective jurors for cause, or they can use what are called "peremptory challenges". To have a prospective juror dismissed for cause, a party has to convince the judge that the prospective juror would not be able to fairly judge the case. A peremptory challenge can be used without any justification. Neither type of dismissal can be done on the basis of race, but that's difficult to enforce in the case of peremptory challenge, as a party is free to give any non-race reason they feel like, regardless of how relevant.
When it comes to grand juries, I found conflicting information.
The Legal dictionary says:
Jurors responding to the grand jury summons are randomly called and put through the voir dire selection process in which the attorneys for the case question prospective jurors
However, it also says:
The accused has no right to present his case, and in many cases is not even made aware the hearing is taking place.
If the accused is not aware of the hearing, it would seem to follow that they would not participate in voir dire, so this seems that the conclusion is that only the prosecution participates in voir dire.
On the other hand, houmatoday.com says:
There is no voir dire
So either there is no voir dire, in which case no prospective jurors are dismissed, for race or any other reason, or there is voir dire, in which they can be dismissed, but not on the basis of their race.
If commenters clarify this issue, I will edit accordingly, but the answer to the main question is the same either way.