Hi @sbgoh ,
Delete the date text from the Date Picker control doesn't mean to clear the selected date.
To implement your needs, you have to add an extra Remove button in the data card to clear the selected date. Please refer to the following steps.
1. Unlock the data card, insert a Cancel icon
2. Set Icon.OnSelect: Set(vardate,Blank())
3. Set DatePicker.DefaultDate: If(IsBlank(vardate),vardate,Parent.Default)
4. Set DatePicker.OnChange: Set(vardate,1)
5. Enable the "Formula Level error management" in Advanced Setting. (Important!)

Hope this helps.
Sik