Don't look so sad.
そんな悲しそうな顔をするな
Don't lose (any) sleep over it.
あまり心配するな
Don't make snap [hasty] decisions.
決断を焦るな
Don't make up excuses.
言い訳するな
Don't mention the matter to anyone.
それをだれにもしゃべらないでくれ
Don't mind him. He's always like that.
気にしないで,彼はいつもあんな調子だから
Don't mind me.
おかまいなく(続けてください,など)
Don't misunderstand (me).
誤解しないでください
Don't mix me up in the matter.
そこには巻き込まないでくれ
Don't morning me.
(朝帰りして)「おはよう」なんて言えた義理か