By "death", I assume you mean senescence: the natural biomolecular attrition that inexorably leads to organismal death absent of outside causes.
It is true that turtles can live for almost 200 years and some plants can live for thousands of years. If we are essentially, biochemically the same, we could in theory overcome our biochemical "bugs" to achieve negligible senescence. So, we'd live forever.
Unfortunately, that's a hard problem because we didn't design the system -- unlike computers and programing languages -- and we're trying to reverse engineer an insanely complex system created by the massively parallel process of natural selection acting on random mutation. And we're hampered by things like IACUC.
Computational capacity may double every 2 years, but a mouse still has a generation time of 3 months, just like it did a million years ago. That's why biomedical progress (frustratingly) doesn't progress at Moore's Law, and you can't just throw money or engineering talent at the problem.
So yeah, focus on "death" as a biochemical problem, but "focusing on death" won't solve the problem at the same pace as focusing your engineering talent on a human engineering problem. The natural sciences are much more stochastic, and there's no clear path to immortality.