Stop Illegal Reentry Act or Kate's Law This bill increases criminal penalties for certain aliens who illegally reenter the United States after removal or exclusion. Generally, an alien who had been denied entry into or removed from the United States and who later enters or attempts to enter the United States without prior approval from the Department of Homeland Security shall be fined, imprisoned for up to five years, or both. Current law requires a fine, imprisonment for up to two years, or both, for such an alien. An alien who had been denied entry or removed three or more times and who later enters or attempts to enter the United States shall be fined, imprisoned for up to 10 years, or both. An alien who was convicted of an aggravated felony or convicted at least two times before removal or departure and who subsequently enters or tries to enter the United States shall be imprisoned at least five years and for up to twenty years, and may also be fined. Currently, there is no minimum term of imprisonment for an alien who reenters after a conviction for an aggravated felony, and there are no criminal penalties for a reentering alien who had been convicted at least two times (other than the penalties for illegal reentry generally).