H.RES.776 - Federal Government - Amending the Rules of the House of Representatives to require that rescission bills always be considered under open rules every year, and for other purposes.

Cut the Unnecessary Tab Resolution, or CUT Resolution - Amends Rule XIII (Calendars and Committee Reports) of the Rules of the House of Representatives to prohibit the Committee on Rules from reporting a rule or order that would limit any amendment that would otherwise be in order to a rescission bill.

Amends Rule X (Organization of Committees) to require the House Budget Committee, whenever a rescission bill passes the House, to reduce the applicable committee allocations by the total amount of resulting reductions in budget authority and outlays.

Amends Rule XIII to require the Majority Leader to introduce a rescission bill by certain dates in each session. Makes any motion to discharge the committee from consideration of such a bill privileged 10 legislative days after its introduction, if it was not introduced by one of the deadlines.

Makes it out of order to offer any amendment to a rescission bill unless it increases the amount of budget authority to be rescinded.

Amends Rule XXI (Restrictions on Certain Bills) to make it out of order to consider any rescission bill, its conference report, or amendment, unless: (1) such bill or conference report is made available to Members and the general public on the Internet for at least 48 hours before its consideration; (2) an amendment to such measure made in order by a rule is available within one hour after the rule is filed; or (3) an amendment under an open rule is made available immediately after being offered in a format searchable and sortable.

Requires amendments to rescission bills to be germane.