All DR is multiplicative, not additive. This means that 10% DR from any source reduces your damage taken by 10% compared to the damage you’d take without that source of DR.
The formula is DamageTaken = RawDamage * (1 - DR1%) * (1 - DR2%) * (1 - DR3%) ...
Specifically for your example, you take 15% reduced damage from Demonic Wards, meaning you take 1 - 0.15 = 85%
of the raw damage. 10% versatility is applied as an additional source of DR, meaning you take 0.85 * (1 - 0.1) = 0.85 * 0.9 = 76.5%
. So yes, they net to 23.5% DR, as you guessed.
This is important, though. If this weren’t the case, DR would get more potent the more sources you had of it. If they were additive, for example, then a paladin (ignoring their DR from armor and Consecrate) with Guardian of Ancient Kings up (50% DR) would go from 50% to 60% DR with 10% versatility. This would mean that versatility reduced their damage by 1 - (1-0.6) / (1 - 0.5) = 1 - 0.4 / 0.5 = 1 - 0.8 = 20%
. Double the normal effectiveness. That would be very bad, because it would make stacking DR absurdly powerful, which would require nerfing all sources of DR to prevent them from getting out of control when stacked (and thus making them pretty meh when used alone).
When stacked multiplicatively, they also intuitively make more sense. Regardless of how much DR you currently have, activating an ability that grants you 40% DR (say, Fiery Brand) reduces your damage intake by 40% of the damage you are currently taking.
This also effectively means you can treat each source of DR in isolation. Regardless of your DR from other sources, 10% DR from versatility means you need 10% less external healing to keep up (and 25% less self-healing, since you take 10% less damage and self-heal for 20% more).
Edit: that said, I should point out that versatility is additive with itself for DR. That actually makes it, for the purposes of DR, slightly better the more of it you have. For example, your first 1% versatility reduces your current damage intake by 1%. If you already have, say, 20%, however, your next 1% reduces your current damage intake by 1 - 0.79 / 0.80 = 1.25%
. Unfortunately, this effect is very small over the range of viable values, so it can largely be ignored.