Tim Stauffer is not the worst newly acquired relief pitcher for the Twins the last decade, but...

He has Juan Morillo to thank for that (and it is close).   Here is a list of the relief pitchers newly acquired by the Twins who had an xFIP higher than 5, in their first year with the club, during the last 10 years.  The list includes traded players, major league and minor league free agents.

Stauffer has some good company.  (List by decreasing xFIP)

Juan Morillo 2009: ERA 22.50, FIP 13.10, xFIP 9.88, WHIP 3.00
Tim Stauffer 2015: ERA 8.38, FIP 8.61, xFIP 6.48, WHIP 2.28
Esmerling Vasquez 2012: ERA 5.68, FIP 4.93, xFIP 6.47, WHIP 1.61
Luis Perdomo 2012: ERA 3.18, FIP 4.62, xFIP 5.83, WHIP 1.59
Carmen Cali 2007: ERA 4.71, FIP 5.72, xFIP 5.67, WHIP 1.81
Randy Flores 2010: ERA 5.29, FIP 4.74, xFIP 5.62, WHIP 3.27
Eric Hacker 2011: ERA 0.00, FIP 4.53, xFIP 5.47, WHIP 1.50
Jeff Gray 2012: ERA 5.17, FIP 5.84, xFIP 5.42, WHIP 1.54
Sean Henn 2009: ERA 7.15, FIP 6.19, xFIP 5.40, WHIP 1.50
Josh Roenicke 2013: ERA 4.35, FIP 4.64, xFIP 5.30, WHIP 1.60
Phil Dumatrait 2011: ERA 3.92, FIP 5.71, xFIP 5.27, WHIP 1.69
Jim Hoey 2011: ERA 5.47, FIP 5.58, xFIP 5.25, WHIP 1.91
Matt Guerrier 2014: ERA 3.86, FIP 3.92, xFIP 5.22, WHIP 1.43
Dusty Hughes 2011: ERA 9.95, FIP 7.53, xFIP 5.01, WHIP 2.13