Big game tags, including wolf tags and mountain lion tags, expire on 12/31 of the year of purchase. For example, all 2013 tags expired 12/31/13 and are not valid for use in 2014.
Specific to mountain lion and wolf hunting--the seasons run from fall of one year through spring of the next. The tag you purchase for fall hunting expires on 12/31. If you wish to continue hunting the rest of the season (Jan 1 to close of season), you must purchase a new license and tag for the new calendar year.