Since God invites man to reason on His Word (Isaiah 1:18), we must know that His Word is reasonable. The quotation in the question is unreasonable. But is it a part of God's Word? We answer, No. Mark's Gospel originally ended with Mark 16:9; the additional verses (10-20 inclusive) which includes the above quotation, are not found in the oldest manuscripts of the Bible. Scholars are agreed that the addition was made about 600 years after Mark's Gospel was written, and hence the quoted words are not part of the Gospel, and we know them to be untrue. To sanction them, now that we know about them, would be to join with those who wrote them in adding to the Word of God (Revelation 22:18,19). Human experience shows that not even the best of Christians can, with impunity, "Take up serpents and drink deadly poison."

We have answered a similar question presented to us in this way:

Over the centuries, other texts were also incorporated into manuscripts. These corruptions may have initially been marginal notes which well-meaning scribes included when copying older manuscripts.  By 1516 AD, the date of the Textus Receptus, different manuscripts featured three distinct endings to the book of Mark. Erasmus, the scholar who established the Textus Receptus, chose to use the ending translated in the NKJV.

To those who believe in the authenticity of Mark 16:9-20, we would encourage them to consider verse 18, “they will take up serpents; and if they drink anything deadly, it will by no means hurt them…” Nowhere else in the Bible are these concepts taught. But Deuteronomy 19:15 teaches, “Every matter must be established by the testimony of two or three witnesses.” The Apostle Paul quotes the same scripture in 2 Corinthians 13:1 as proof of his argument. 

Therefore, biblical doctrines should also be established by at least two or three scriptures. For example, the doctrines of Christ’s sufferings and of earthly restitution were taught by all God’s prophets. Acts 3:18, 24 (NKJV), “But those things which God foretold by the mouth of all His prophets, that the Christ would suffer, He has thus fulfilled…Yes, and all the prophets, from Samuel and those who follow, as many as have spoken, have also foretold these days (of restitution at Christ’s 2nd advent).” Multiple scriptures testify to these truths.

Since verse 18 is not supported by other scriptures, we would not act on the basis of these questionable verses.