In data-browser I don't think it's possible to delete a date value, I couldn't find a way to do it at least.
And now that Parse.com will not be maintained anymore(in 01/01/2017 it will shut down), I don't think this may come up as a feature.
My solution to this problem was to make a request to this register and use unset. It gets a bit more of work but solves the problem.
I don't know if you're using parse with Javascript but it can be really easy to adapt to other enviroments.
In Javascript this script should do the trick:
var DateUpdate = Parse.Object.extend("MyTableOnParse");
var dateUpdateEdit = new Parse.Query(DateUpdate);
dateUpdateEdit.equalTo("objectId",myObjectId);
dateUpdateEdit.first({
success: function(object)
{
object.unset("saleDate");
object.save({
success: function(updatedObject)
{
console.log("Data deleted");
}
})
}
});