Break off has two meanings:

1. To end abruptly, either temporarily or permanently. 2. To remove a piece from a whole by breaking or snapping.

Your example, break off one's plans, is the first meaning.

Browsing COCA, we can find plenty of examples:

What caused you to break off the last engagement?
Break off communication with the Earth shuttle at once.
... prompting him to break off relations with his Venetian publisher in 1730.
... demanded that their leaders break off the negotiations.

Break (definitions 6, 7, 8 in OALD) can be used without off in a similar sense, meaning to "end something" by interruption, forceful action (as if snapping), or by severing a connection. For example, you can break someone's fall, break a fast, break a tie (to determine a winner) or break all ties (to stop talking to someone).

Break off has two meanings:

1. To end abruptly, either temporarily or permanently. 2. To remove a piece from a whole by breaking or snapping.

Your example, break off one's plans, is the first meaning.

Browsing COCA, we can find plenty of examples:

What caused you to break off the last engagement?
Break off communication with the Earth shuttle at once.
... prompting him to break off relations with his Venetian publisher in 1730.
... demanded that their leaders break off the negotiations.

Break (definitions 6, 7, 8 in OALD) can be used without off in a similar sense, meaning to "end something" by interruption, forceful action (as if snapping), or by severing a connection. For example, you can break someone's fall, break a fast, break a tie (to determine a winner) or break all ties (to stop talking to someone).