How do you cut different things in Chinese?
Cut things with a sickle (鎌刀) or in a motion similar to using a sickle is 割 (cut)


Example: 割草，割辫，割头，割尾巴 (cut grass, cut braid, cut head, cut tail) 


  Cut things with scissors (剪刀) or cut things with a scissoring motion is 剪(cut)


Example: 剪头发，剪草，剪布，剪指甲 (cut hair, cut grass, cut cloth, cut finger nail)


  Cut things with a knife (刀), especially Kitchen knife (廚刀) or a motion similar to using a Kitchen knife is 切 (cut) 


Example: 切菜，切饼，切水果，切肉 (Cut vegetables, cut cake, cut fruit, cut meat)


  Cut things with an axe or other cutting tool using similar motion as using an axe is 砍 (cut; hack)


Example: 砍头，砍木，砍柴，砍蔗 (cut head, cut wood, cut firewood, cut sugar cane)


  斩 (cut; hack) is similar to 砍 but mostly with a knife or other bladed weapons more slender than an axe


Example: 斩頭，斩木，斩柴，斩蔗 (cut head, cut wood, cut firewood, cut sugar cane) 

Both 砍 and 斩 contains the meaning of 劈 (hack)


  刮 is 'to scratch' or 'to shave'


Example:刮骨，刮须，刮皮，刮毛 (Bone scraping, shaving bread, skin scraping, shaving body hair)

To determine which character to use, just think of what tool or what motion you use to cut the object, for example: a basketball. How do you cut a basketball in half? Certainly not by 砍 (to hack) or 割 (to slice). The correct tool is 鋸(saw) and the motion is called "to saw" (鋸) as in 鋸开(saw open) 鋸断 (saw apart)


  if there's one more character worth being added here, let me know!


削 (削皮刀- peeling knight; 削掉- to slice/ peel off)

闸 (闸刀- chopper switch; 闸断- to chop apart)

 (刀- box cutter; 开 - to slice open/ to cut open)

剃 (剃刀- shaving blade; 剃掉 - to shave off)