The polite negative: ません

Replace ます with ません, keeping everything before it: 飲のみます → 飲のみません, 食たべます → 食たべません, 行いきます → 行いきません.

This change works across all three verb groups. Even 来きます becomes 来きません. The different group rules matter when making the ます form; once you have that form, the negative ending is the same.

肉にく を 食たべません is a polite way to say “I don’t eat meat.” Depending on context, a ません sentence can describe a habit or a future action you will not do. There is no separate word corresponding to English “don’t.”