Keep Our Communities Safe Act of 2013

Keep Our Communities Safe Act of 2013 - Amends the Immigration and Nationality Act (INA) to revise provisions regarding the detention and removal of aliens ordered removed.

Begins the removal period on the latest of: (1) the date the removal order becomes administratively final; (2) the date the alien is taken into Department of Homeland Security (DHS) custody if the alien is not in DHS custody on the date the removal order becomes administratively final; or (3) if the alien is detained or confined (except under an immigration process) on the date the removal order becomes administratively final, the date the alien is taken into DHS custody after the alien is released from detention or confinement.

Extends the removal (and detention) period beyond 90 days if: (1) the alien fails or refuses to comply with the removal order or to fully cooperate with DHS efforts to establish the alien's identity and carry out the removal order; (2) a court, the Board of Immigration Appeals, or an immigration judge orders a stay of removal of an alien who is subject to a final removal order; (3) DHS transfers custody of the alien to another federal agency or to a state or local agency; or (4) a court or the Board of Immigration Appeals orders a remand to an immigration judge or the Board of Immigration Appeals while the case is pending a decision on remand.

Begins a new removal period in the case of such an extended removal on the date: (1) the alien makes all reasonable efforts to comply with the removal order or to fully cooperate with DHS efforts to establish the alien's identity and carry out the removal order, (2) the stay of removal is no longer in effect, or (3) the alien is returned to DHS custody.

Requires mandatory detention for an alien who is inadmissible or deportable under specified criminal or terrorist grounds.

Directs the Secretary to establish a detention review process for cooperative aliens.

Authorizes DHS to detain indefinitely, subject to six-month review, an alien under removal order who cannot be removed if: (1) the alien will be removed in the reasonably foreseeable future; (2) the alien would have been removed but for the alien's refusal to cooperate with DHS identification and removal efforts; (3) the alien has a highly contagious disease that poses a public safety threat; (4) release would have serious adverse foreign policy consequences or would threaten national security; (5) release would threaten the safety of the community or any person and the alien has been convicted of either one or more aggravated felonies or crimes of violence and, because of a mental or personality condition, is likely to engage in future acts of violence; or (6) release would threaten the safety of the community or any person and the alien has been convicted of one or more aggravated felonies.

Authorizes unlimited detention of certain aliens during removal proceedings.

Subjects a criminal alien to mandatory DHS detention upon release without regard to whether the alien's release is related to: (1) certain activities, offenses, or convictions under INA; (2) whether the alien is released on parole, supervised release, or probation; or (3) whether the alien may be arrested or imprisoned again for the same offense.

Limits the Attorney General's (DOJ) review of DHS custody determinations to whether the alien may be detained, released with no bond, or released on bond of at least $1,500.

Limits the Attorney General's review of DHS custody determinations for an alien in certain categories to whether the alien was properly included in such category.