I hope you don't mind _____ at your newspaper.
mind为Vt(及物动词)可加不定词词组，
而且不定词词组可当N和当O用，
为什么不能用mine to look 呢？
要用 my looking

嗯嗯谢谢各位指正

my looking...newspaper是动名词词组，当受词用不是所有及物动词后面都可加to V，像mind是固定加v-ing

原句可写成mind that I look at your newspaperthat子句改成动名词词组后，就变成my looking at...