Yes..hack them off or get rid of the tree.

the tree pretty big , we trim the branches lower last year .

Conventional wisdom is that it is better to pull suckers off than cut them.

Yes... pull in the garden or dig them up for a year of freedom but the ones you show coming off the trunk can't be pulled.

Most often they can. But it's mostly a snap-off-from-the trunk rather than pull out of the soil.