Last week, North Korea's Army said it would _______________all roads and railways connected to South Korea and ________________border areas, according to state media KCNA.

"Cut" is the appropriate word to indicate severing connections like roads and railways, and "fortify" correctly conveys strengthening or securing border areas. The other options do not fit the context: "Lay off" means to stop employing people, and "embattle" means to prepare for war, which doesn't match the specific actions described. "Trench off" and "mitigate" don't work; "mitigate" means to reduce or alleviate, which doesn’t align with securing borders. "Slack" means to reduce activity, and "gird" refers to preparing for a challenge but doesn't fit here. Thus, option 1 is the correct choice.