We present results from spectroscopic observations with the Michigan/Magellan Fiber System (M2FS) of 147 stellar targets along the line of sight to the newly-discovered `ultrafaint' stellar systems Tucana 2 (Tuc 2) and Grus 1 (Gru 1). Based on simultaneous estimates of line-of-sight velocity and stellar-atmospheric parameters, we identify 8 and 7 stars as probable members of Tuc 2 and and Gru 1, respectively. Our sample for Tuc 2 is sufficient to resolve an internal velocity dispersion of 8.6+4.4−2.7 km s−1 about a mean of −129.1+3.5−3.5 km s−1 (solar rest frame), and to estimate a mean metallicity of [Fe/H]= −2.23+0.18−0.12. These results place Tuc 2 on chemodynamical scaling relations followed by dwarf galaxies, suggesting a dominant dark matter component with dynamical mass 2.7+3.1−1.3×106 M⊙ enclosed within the central ∼160 pc, and dynamical mass-to-light ratio 1900+2200−900 M⊙/LV,⊙. For Gru 1 we estimate a mean velocity of −140.5+2.4−1.6 km s−1 and a mean metallicity of [Fe/H]=−1.42+0.55−0.42, but our sample does not resolve Gru 1's velocity dispersion. The radial coordinates of Tuc 2 and Gru 1 in Galactic phase space suggest that their orbits are among the most energetic within distance ≤300 kpc. Moreover, their proximity to each other in this space arises naturally if both objects are trailing the Large Magellanic Cloud.