Since it's called a "lift", the most logic approach is indeed to lift the bar up, but for some this can actually result in more of a pull with the weaker bodyparts.
When the load gets heavier, some of most common mistakes are pulling too much with the arms and rounding the upper/lower back.
Perhaps these few tricks will help to add more weight to your PR:
- Instead of lifting up, try to imagine pressing the ground down with your legs. This will automatically force you to focus on pressing from the legs instead of pulling with your arms and back.
- That being said, view your arms simply as tools to hook onto the bar.
- Mark a spot on the ground about 3 feet in front of you to focus on. Keep your eyes on that spot during the entire lift. This will keep your head in a neutral position. The psychology of lifting up often results in people looking up as well, which causes a "break" in your spinal support.
- Grip - if the hook grip is not your best friend, consider having a mixed grip (see Franco) Having a mixed grip prevent the bar from rolling out of your hands. It could be a personal preference, but we like have our dominate hand with the palm towards the body. Just play around with it what works best for you.
More talk on deadlifts by Mark Rippetoe: