What do you mean by seriously damaging my store? You can delete products in bulk using Magmi. Once the products are deleted you should create a new site map and submit it to the Google.

Yes, deleting products in bulk should affect the Google ranking.

If you delete products in bulk then Google will redirect the users to the 404 pages for those products. You may create 301 redirects for the deleted products to their category pages to avoid 404 error.

It is better to take advise from a professional SEO expert.