As mentioned, graptolites are an uncommon component of the local fauna. They do pop up from time to time, though, and their thin dark saw blade fossils are quite distinctive if you get a large enough chunk. Reports of graptolites in the Twin Cities go back almost to the beginning of local geology, actually. Shumard (1852) reported graptolites from a bluff about a half-mile downstream from Fort Snelling, in what would now be considered the lower Platteville Formation. Winchell and Schuchert (1895) provided illustrations for three species, Climacograptus typicalis, Diplograptus pristis?, and Diplograptus putillus. All of their cited specimens came from outside the metro, and apparently from higher stratigraphically than virtually all metro rocks, with C. typicalis from what would now be the Cummingsville Formation and the other two from what would now be the Dubuque Formation, per the stratigraphic table in Winchell and Ulrich (1897). Stauffer (1930) found abundant black fragments of graptolites in a particularly calcareous layer low in the Decorah Shale in rocks recovered from a heating shaft dug for Northrop Auditorium. Stauffer and Thiel (1941) observed C. typicalis in what would now be the Mifflin Member at Lock and Dam 1, on the Ramsey County side. Their lists reported three following species in the Platteville Formation and Carimona Member (their Spechts Ferry). All three were listed under Hydrozoa, the group that includes relatives of corals and jellyfish, which was a reasonable enough hypothesis at the time (before the discovery of pterobranch affinities, graptolite relationships were a free-for-all):
Climacograptus typicalis (Pl, Ca)
Climacograptus (Mesograptus) putillus (Pl)
Diplograptus amplexicaulis? (Pl)
(More graptolites are known from older rocks a bit farther afield in Minnesota. Ruedemann  described several species from the Upper Cambrian St. Lawrence Formation of Afton.)
|From Winchell and Schuchert (1895). This looks kinda like at least one of the examples in the following photo, but you should always be wary of diagnosing your fossils via photos and plates.|
|A University of Minnesota piece with a few graptolites (look for the things that look like saw blades on sticks. Mouse-sized hacksaws.).|
Mitchell, C. E., M. J. Melchin, C. B. Cameron, and J. R. Maletz. 2013. Phylogenetic analysis reveals that Rhabdopleura is an extant graptolite. Lethaia 46(1):43–56.
Ruedemann, R. 1933. The Cambrian of the upper Mississippi Valley, part III, Graptolitoidea. Milwaukee Public Museum Bulletin 12(3):307–348.
Shumard, B. F. 1852. Geological report of local, detailed observations, in the valleys of the Minnesota, Mississippi, and Wisconsin rivers, made in the years 1848 and 1849, under the direction of David Dale Owen, United States Geologist, by B. F. Shumard, head of subcorps. Pages 481–531 in Owen, D. D. Report of a geological survey of Wisconsin, Iowa, and Minnesota; and incidentally of a portion of Nebraska Territory. Lippincott, Grambo & Co., Philadelphia, PA. Available at http://archive.org/details/mobot31753000174885 or http://books.google.com/books?id=Y_ZYAAAAYAAJ.
Stauffer, C. R. 1930. Conodonts from the Decorah Shale. Journal of Paleontology 4(2):121–128.
Stauffer, C. R., and G. A. Thiel. 1941. The Paleozoic and related rocks of southeastern Minnesota. Minnesota Geological Survey, St. Paul, MN. Bulletin 29.
Winchell, N. H., and C. Schuchert. 1895. Sponges, graptolites, and corals from the Lower Silurian in Minnesota. Pages 55–95 in Lesquereux, L., C. Schuchert, A. Woodward, E. Ulrich, B. Thomas, and N. H. Winchell. The geology of Minnesota. Minnesota Geological and Natural History Survey, Final Report 3(1). Johnson, Smith & Harrison, state printers, Minneapolis, MN.
Winchell, N. H. and E. O. Ulrich. 1897. The lower Silurian deposits of the Upper Mississippi Province: a correlation of the strata with those in the Cincinnati, Tennessee, New York and Canadian provinces, and the stratigraphic and geographic distribution of the fossils. Pages lxxxiii–cxxix in L. Lesquereux, C. Schuchert, A. Woodward, E. Ulrich, B. Thomas, and N. H. Winchell. The geology of Minnesota. Minnesota Geological and Natural History Survey, Final Report 3(2). Johnson, Smith & Harrison, state printers, Minneapolis, Minnesota.