Well, without more context, it's hard to be precise. 'Blow' could be used in a metaphorical sense in a 'blow love story'. Maybe it means a love story that has a sudden, impactful moment that changes the course of the relationship, like a blow to the status quo. For example, a couple who were happily in love until a big argument or a major life change, like a job transfer to a different country, blew their relationship off course.
A 'blow love story' might be a story where love is as fragile as a bubble that can be 'blown' away. It could involve characters who fall in love quickly but then face challenges that make their love seem tenuous. For instance, in a story, two young people meet at a music festival and fall head over heels for each other. But then, they discover that they come from very different backgrounds and families that oppose their relationship. This 'blow' to their new - found love creates a complex and perhaps tragic love story.
A 'blow love story' could potentially be a story about a love that is disrupted or 'blown' away, perhaps by unexpected events or misunderstandings. It might also refer to a love story that is as light and fleeting as a gentle blow of wind.