When you have your rows selected which you want to clear
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while holding ALT press on the column name you want to remove the values from
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you should end up values selected only from that column. Then you can press delete to remove the values (or set them as missing)
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But I wouldn't really suggest doing this in JMP. Depending on what you are doing and the format of your data there might be better options such as hide and exclude row and set missing value codes column property.
-Jarmo