Jae - One quick solution is to use "Custom Split" feature. By this, Tableau splits "Product" & "Service" from everything after "-" and creates a new column, which you can use as a filter. Link below should help you,
Hope this helps.
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you can create another layer of Filter like
if contains([current field],'"PRODUCT") then "Product"
elseif contains([current field],'"SERVICE") then "Service"
Then, select this layer first, then you can put [current field]'s filter setting to "Only relevant value"
If you could attach sample data as twbx, we can provide the solution more easily.