帮忙解释下这句的英语语法例句：i used a knife to cut the butter 和 i used a k

帮忙解释下这句的英语语法
例句：i used a knife to cut the butter 和 i used a knife to cut the butter with 的区别在哪里?加with对么?
同样还有write with clean with等,都一样么?
我正在读一篇英文的同人文,看到这句：
“He walked into the bathroom and pulled out some tissue to clean himself off with.”
语法结构都对么?