You can use a variable in the Default property on you date field, call it "varDate" or whatever you feel fit.
Then your solution would look something like this
If(DataCardValue61_3.Selected.Text = "Closed", Set(varDate, Now()), Set(varDate, Blank()))
What it does is to check if the status field is set to closed and if it is, it sets the date field to current time, else it blanks out the date field instead.