What code /std is applicable? An increase in maximum time between root bead and second bead is essential variable in API 1104.
I will not suggest surface cleaning by grit blasting, if needed to continue without cutting it off due to large diameter (e.g. 1meter dia), you may do power brush cleaning to be followed by PT/MT to ensure no surface defect before welding can resume.
TJGOH,
It does depend on the COC, and what material is being welded and what the application is. But in the absences of that, the following are my thoughts. Some ASME codes require 30% in the joint before you can leave it, for certain materials. P3,P4,P5A, P5B, P6 and P15E. If it's just P1 to P1 material, I would brush it clean, visually inspect and if you find no visible discontinuities, finish it.