Let the dead bury the dead this time, Mr Finch. Let the dead bury the dead.

Tom Robertsen could be considered a mockingbird.  The fact that Mr. Ewell (who effectively killed him) has died could be seen as punishment.  Mr. Tate believes that no one should be tried for killing him.  He got what he deserved.  Even though the evidence points to Mr. Radley killing Mr. Ewell, Mr. Tate then makes Mr. Ewells death out to be accidental, to protect Mr. Radley.  Mr. Tate metaphorically “buries” the case.  He doesn't want anymore people to be hurt.

The line: “let the dead bury the dead” is also a line in the bible which Jesus Christ tells a disciple to come with him.  The man says ok, but asks to bury his father first.  Jesus Christ tells the man ‘come with me and let the dead bury the dead’. Jesus Christ is telling the disciple to move on, to let those who are still upset to mourn.  It is similar to what Mr. Tate means.