If XeLaTeX is the only format that satisfies your typesetting needs -- in particular, if you can't use LuaLaTeX -- you have two options for suppressing the tt ligature while not also turning off all "common" ligatures entirely:
Insert what TeX calls an implicit kern (of zero width) between the two t characters:
rot\kern0pt ten % note: no space between "\kern" and "0pt"
Insert what TeX calls an explicit kern (also of zero width) between the two t characters:
rot\/ten, rot\kern 0pt ten % note the space between "\kern" and "0pt"
The "italic correction" \/ is a type of explicit kern. By the way, the italic correction method will not give a satisfactory result if the word in question is, in fact, typeset in italics.
Note that this will have to be done separately for each and every instance of "tt".
Final note/comment: The fact that words containing the tt ligature can't be searched in the pdf file if it's compiled via XeLaTeX could be a bug in the implementation of Linux Libertine O under XeLaTeX. First, words that contain the more common "Common" (pun intended) ligatures ff, fi, fl, and ffl are, in fact, searchable if the document is compiled via XeLaTeX. Second, the font family Palatino nova also features the tt ligature. When I compile the MWE below with Palatino nova instead of Linux Libertine O, I encounter no difficulties searching for words that contain the tt ligature (or, for that matter, words that contain the ff, fi, fl, ffi, and ffl ligatures).

% !TEX TS-program = xelatex
\documentclass{article}
\usepackage{fontspec}
\setmainfont[Ligatures={TeX,Common}]{Linux Libertine O}
\begin{document}
implicit kern (\verb+rot\kern0pt ten+): rot\kern0pt ten \& \emph{rot\kern0pt ten}
explicit kern (\verb+rot\/ten+): rot\/ten \& \emph{rot\/ten}
\verb+ro{t}{t}en, rot{}ten+: ro{t}{t}en, rot{}ten --- tt ligature still there!)
\end{document}
ro{t}{t}en, to avoid the ligature? Evenro{t}tenshould work. – Steven B. Segletes Jan 08 '14 at 19:10ttligature remain searchable if the file is compiled by LuaLaTeX. – Mico Jan 08 '14 at 19:10rot{}tenorro{t}{t}ento break up thettligature works under pdfLaTeX, this method does not work under either XeLaTeX or LuaLaTeX. :-( – Mico Jan 08 '14 at 19:19{t}doesn't always work under tex/pdftex either (it depends on details of linebreaking) early editions of the TeXbook suggested that but it was chnaged to suggest using \kern – David Carlisle Jan 09 '14 at 00:43