The manchineel tree, or little death apple hippomane mancinella is a highly toxic tree native to the Caribbean islands, ranging as far north as southern Florida.

The manchineel is reportedly so toxic that rain falling from the leaves of the tree can cause severe chemical burns. Smoke from its burning wood causes serous pneumonia. Its sap can cause blindness. It is used by some indigenous Caribbean people to poison hunting arrows, and is believed to have been used on the arrow that killed Ponce De Leon. Its notorious properties have been used in literature (eg. include Flaubert's Madame Bovary, Steinbeck's The Pearl) as a plot device.

Upon settling the Everglades, the new inhabitants quickly discovered the manchineel and set about destroying the tree wherever it was found. Although it still exists on several Caribbean islands (it is salt tolerant, and its root system is excellent at stabilizing sand), it is marked, with a red band around the trunk on trees on the French Antilles, and a warning sign on Curaçao. Please note, it is unmarked on many other islands, so if you plan on hiking, bring along a local guide to train you to recognize it.

In the Everglades, one small remote grove of manchineel trees still exists. It is marked on maps, and the trees are marked. It is listed as endangered in Florida, but "carefully controlled" might be a better term.

That's what leaps to my mind in regards to eradicated plant species.

EDIT: Anecdotally, the tree's fruit, or "beach apples" were said to be deadly. I located one modern tale , from a researcher, Nicola H. Strickland, who reports the fruit to be pleasantly sweet, with a strange peppery after effect that quickly progresses into a "burning, tearing sensation, tightness of the throat.". Strickland suffered several days of painful symptoms, but the ingestion of a small bite of the fruit was not fatal.