How to make the caption of table* left align

Probably you are more satified with the following table:

\documentclass[a4paper,fleqn]{cas-dc}

\usepackage{booktabs}

\usepackage{natbib}
\setcitestyle{authoryear,round}

\begin{document}
\begin{table*}[width=.95\textwidth,cols=13]
\caption{The performance evaluation of different models on test set.}\label{tbl3}
\begin{tabular*}{\tblwidth}{lCCCCCCCCCCCC}
\toprule
Method & \multicolumn{3}{c}{GSN}                       & \multicolumn{3}{c}{LS}                        & \multicolumn{3}{c}{OTHERS}                    & \multicolumn{3}{c}{Avg.}                      \\ 
\cmidrule{2-4} \cmidrule{5-7} \cmidrule{8-10} \cmidrule{11-13}
                       & P(\%)         & R(\%)         & F1(\%)        & P(\%)         & R(\%)         & F1(\%)        & P(\%)         & R(\%)         & F1(\%)        & P(\%)         & R(\%)         & F1(\%)        \\ 
\midrule
J48                                          & 67.5          & 64.4          & 65.9          & 64.5          & 73.1          & 68.5          & 86.1          & 84.7          & 85.4          & 79.3          & 79.1          & 79.2          \\
\bottomrule
\end{tabular*}
\end{table*}

\end{document}

Building on @MadyYuvi's comment, I would suggest that you not load the caption package and, instead, issue the directive

\setlength\FullWidth{\textwidth}

before \begin{table*}. (If you want to make scope of this directive global for the entire document, place it in the preamble.) And, to make the table occupy the full width width (and no more than that!), use a tabular* environment instead of a tabular environment.

I would also recommend that you (a) give the table a more open "look" by omitting all vertical bars and using the macros of the booktabs package to create well-spaced horizontal lines and (b) provide more visual structure to the header material by placing the information about unit of measurement to a separate row.

\documentclass[a4paper,fleqn]{cas-dc} 
\usepackage{booktabs}
\shorttitle{Thoughts}

\begin{document}
\begingroup
\setlength\FullWidth{\textwidth}
\begin{table*}
\setlength{\tabcolsep}{0pt}
\caption{Performance evaluation of various models on test set.}\label{tbl3}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} l *{12}{c} }
\toprule
Method
& \multicolumn{3}{c}{GSN} & \multicolumn{3}{c}{LS} & \multicolumn{3}{c}{Others} & \multicolumn{3}{c}{Avg.} \\ 
\cmidrule{2-4} \cmidrule{5-7} \cmidrule{8-10} \cmidrule{11-13}
& P & R & F1 & P & R & F1 & P & R & F1 & P & R & F1 \\ 
& (\%) & (\%) & (\%) & (\%) & (\%) & (\%) & (\%) & (\%) & (\%) & (\%) & (\%) & (\%) \\
\midrule
J48 & 67.5  & 64.4  & 65.9  & 64.5  & 73.1  & 68.5  & 86.1  & 84.7  & 85.4  & 79.3  & 79.1  & 79.2 \\
Naive Bayes & \\
\dots & \\
\bottomrule
\end{tabular*}
\end{table*}
\endgroup
\end{document}