You have relevant keys in enumitem itself: nosep or noitemsep. Also, instead of adding horizontal space between label and item body for each item, set labelsep in the options. Last, I replaced TeX syntax ({\it…}) with LaTeX syntax (\emph{…}).
Final advice: you should make your definition a theorem-like environment: formatting (boldface) could be pre-defined and numbering would be automatic, making cross-references easy. Imagine what would happen if you should decide to add a definition in the middle of your document.
\documentclass[xcolor=x11names,compress]{beamer}
\usepackage{graphicx}
\usepackage{tikz}
\usepackage{enumitem}
\begin{document}
\textbf{Definition 1.1} A \emph{design} is a pair $(X,\mathcal{A})$ iff:
\begin{enumerate}[label=\em \arabic*., labelsep = 0.5em, leftmargin=1cm, nosep]
\item $X$ is a set of \emph{points};
\item $\mathcal{A}$ is a set of \emph{blocks}.
\end{enumerate}
\vskip4ex
\textbf{Definition 1.1} A \emph{design} is a pair $(X,\mathcal{A})$ iff:
\begin{enumerate}[label=\em \arabic*., labelsep = 0.5em, leftmargin=1cm, noitemsep]
\item $X$ is a set of \emph{points};
\item $\mathcal{A}$ is a set of \emph{blocks}.
\end{enumerate}
\end{document}

topsepas well... – Werner Jul 18 '14 at 03:08enumitemconflict withbeamerfor lists? – Werner Jul 18 '14 at 03:46enumitemis not full compatible withbeamer– skpblack Jul 18 '14 at 04:09