Seaweeds, also known as marine macroalgae, are renewable biological resources that are found worldwide and possess a wide variety of secondary metabolites, including tannins. Drifted brown seaweed (DBSW) is particularly rich in tannins and is regarded as biological trash. The cotton leaf hopper Amrasca devastans (Distant) has caused both quantitative and qualitative losses in cotton production. Drifted brown seaweeds (DBSWs) were used in this study to extract, qualitatively profile, and quantify the levels of total tannins, condensed tannins, hydrolyzable tannins, and phlorotannins in the seaweeds; test their insecticidal activity; and determine the mechanism of action. The largest amount of tannin extract was found in Sargassum wightii Greville (20.62%) using the Soxhlet method (SM). Significantly higher amounts of hydrolyzable tannins (p = 0.005), soluble phlorotannins (p = 0.005), total tannins in the SM (p = 0.003), and total tannins in the cold percolation method (p = 0.005) were recorded in S. wightii. However, high levels of condensed tannins (CTAs) were observed in Turbinaria ornata (Turner) J. Agardh (p = 0.004). A. devastans nymphs and adults were examined for oral toxicity (OT) and contact toxicity (CT) against DBSW tannin crude extract and column chromatographic fractions 1 (Rf = 0.86) and 2 (Rf = 0.88). Stoechospermum polypodioides (J.V. Lamouroux) J. Agardh crude tannin was highly effective against A. devastans using the OT method (LC50, 0.044%) when compared with the standard gallic acid (LC50, 0.044%) and tannic acid (LC50, 0.122%). Similarly, S. wightii fraction 2 (LC50, 0.007%) showed a greater insecticidal effect against A. devastans adults in OT than gallic acid (LC50, 0.034%) and tannic acid (LC50, 0.022%). The mechanism of action results show that A. devastans adults treated with crude tannin of T. ornata had significantly decreased amylase, protease (p = 0.005), and invertase (p = 0.003) levels when compared with the detoxification enzymes. The levels of glycosidase, lactate dehydrogenase, esterase, lipase, invertase, and acid phosphate activities (p = 0.005) of S. wightii were reduced when compared with those of the Vijayneem and chemical pesticide Monocrotophos. In adult insects treated with LC50 concentrations of S. wightii tannin fraction 1, the total body protein (9.00 µg/µL) was significantly reduced (OT, LC50—0.019%). The SDS-PAGE analysis results also show that S. wightii tannin fraction 1 (OT and CT), fraction 2 (OT), and S. polypodioides fraction 2 (CT) had a significant effect on the total body portion level, appearance, and disappearance of some proteins and polypeptides. This study shows that the selected brown macroalgae can be utilized for the safer management of cotton leaf hoppers.