If I own both Utilities but mortgage one, do I get 10x or 4x the die roll in rent from the unmortgaged one?
It says right on the card (emphasis mine):

if BOTH Utilities are owned, rent is 10x the amount shown on the dice

Also, from the Monopoly rules:

No rent can be collected on mortgaged properties or utilities, but rent can be collected on unmortgaged properties in the same group.
The player who mortgages property retains possession of it ...