核心问题
（1）I don't know for sure that he's dead.
(2) I can't tell you for sure.
for sure 意为“肯定”“毫无疑问”，据此我把上面的句子分别译为“我确实不知道他死了”。“我肯定不能告诉你”。不知是否准确？
词典解答
你的两句译文都是错误的。大家知道,actually,definitely,certainly和really既可位于否定范围之内,也可位于否定范围之外(即不被否定)。但是,for sure 和 for certain 却与它们不同,总是位于否定范围之内(即被否定),并且常常成为否定的焦点:
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They don't know for sure (for certain). (CGEL) 他们并不确切知道。
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I can't tell you for sure. 我不能确切地告诉你。
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He couldn't tell for sure from a distance whether it was George or Tom. (DAI) 距离太远，他未能准确地说出那个人是乔治，还是汤姆。
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He didn't know for certain which bus to take. (DAI) 他没有确定究竟是乘哪一部公共汽车。
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I can not say for certain when he will arrive. (ALD) 我不能准确地说出他将何时到达。