I hope you don't mind _____ at your newspaper.
mind為Vt(及物動詞)可加不定詞片語，
而且不定詞片語可當N和當O用，
為什麼不能用mine to look 呢？
要用 my looking

嗯嗯謝謝各位指正

my looking...newspaper是動名詞片語，當受詞用不是所有及物動詞後面都可加to V，像mind是固定加v-ing

原句可寫成mind that I look at your newspaperthat子句改成動名詞片語後，就變成my looking at...