How do I claim tree removal expense on my personal property due to drought/tree death from bark beetle?

You can't claim in your taxes this year. It is a personal expense.

However, you can add the costs to your cost basis for when you sell.

For more information, see page 9 of this IRS publication: https://www.irs.gov/pub/irs-pdf/p523.pdf

Its an upkeep expense and considered home improvement. Because it is dead and dying and a hazard.