Protect the surrounding surfaces
Keenly clean the butcher block area and make sure that there is no more dust or grease on it. Let it dry and then look up & mark for required area by masking it with tape. Idea behind this task is to protect any contiguous countertop, backsplash, cabinets or appliances from hitting of with anything.
Hand scrape the surface
Start scraping off the table with the help of paint scraper. Scraper should be shaped so that it could scrap well. Next smoothly drag scraper in the wood grain directions around the wooden surface in order to remove outer layer (can be scratches, burn marks etc) of table.
In order to remove its stains use solution made of household chlorine bleach mixed & water. Apply it with medium scrub brush for removing the stains. If stains are dark then it will require repeating the process more than one time.
If obstinate stains still remain, you need to get wooden bleach (easily available at hardware and paint markets) and to follow given guidelines on the container.
Wash that area systematically and after that neutralize the area with liquid solution made of water and vinegar.
Sand the surface
For your safety you can wear goggles and mask or gloves. Use a finish sander along with unusual grades of sandpaper until the scratches and cuts vanish. Start sanding with track 80-grit sandpaper, followed by 120-grit sandpaper. After that, take 240-grit sandpaper for finalizing the sanding process and making the surface smooth.