When the root of a tree is cut and tree falls down, its branches and twigs automatically dry up. Similarly, when I have killed this diplomatic Visnu, the demigods, for whom Lord Visnu is life and soul, will lose the source of their life and wither away

Expressions researched:
"When the root of a tree is cut and the tree falls down, its branches and twigs automatically dry up. Similarly, when I have killed this diplomatic Viṣṇu, the demigods, for whom Lord Viṣṇu is the life and soul, will lose the source of their life and wither away"

Srimad-Bhagavatam

SB Canto 7

When the root of a tree is cut and the tree falls down, its branches and twigs automatically dry up. Similarly, when I have killed this diplomatic Viṣṇu, the demigods, for whom Lord Viṣṇu is the life and soul, will lose the source of their life and wither away.

SB 7.2.9, Translation and Purport

When the root of a tree is cut and the tree falls down, its branches and twigs automatically dry up. Similarly, when I have killed this diplomatic Viṣṇu, the demigods, for whom Lord Viṣṇu is the life and soul, will lose the source of their life and wither away.

The difference between the demigods and the demons is here explained. The demigods always follow the instructions of the Supreme Personality of Godhead, whereas the demons simply plan to disturb or kill Him. Nevertheless, sometimes the demons very much appreciate the full dependence of the demigods upon the mercy of the Lord. This is indirect glorification of the demigods by the demons.