You can hide the time formatting from a date field by editing its field configuration and untoggling the option to show time.
If you still need time in this field but only want it not to appear in the group by, I would create a formula field pointed at your date field, remove time formatting, and group by this field instead.
Hope that helps!
If your field is an editable field, I do not recommend changing it to a date only field, as you will loose the time data when you make the change.
You can create a formula field that converts the date/time field to just a date string. The easiest formula is DATESTR(), but there are other variations, especially if you end up with timezone issues.