According to the Minnesota Constitution Article IV, Section 23, a line-item veto (also known as an item veto) is the power of the governor to reject one or more items of appropriation in a bill, while approving the rest of the bill. The Governor can only line-item veto appropriations; the governor cannot line-item veto policy provisions in a bill. A more detailed description of line-item vetoes is in: History of the Item Veto in Minnesota.
If a bill is passed during the last three days of the session, the governor can "pocket veto" the bill by not signing it within 14 days after final adjournment (sine die). Historical data on vetoes and override attempts is available on the Minnesota Legislative Reference Library's webpage: Bills Vetoed.