Yes when needed. Wet, contaminated, or rodent-damaged insulation is removed and disposed of. Dry, clean fiberglass can sometimes be left in place under foam, but most retrofits benefit from removal first.
More detail
Three categories of old insulation. (1) Wet, mold-contaminated, rodent-damaged, or evidently failing insulation: always remove. Cost $0.50-$1.50 per sqft for removal and disposal; local contractors include this in the quote when on-site assessment identifies the need. (2) Dry, clean, structurally-intact fiberglass batts: sometimes left in place when the spray foam is being added on top (e.g., closed-cell on a roof deck above existing fiberglass batts in rafter cavities). The result is a hybrid assembly where the foam provides air seal and the fiberglass adds R-value. Works fine but is less common than full removal. (3) Loose-fill blown cellulose or fiberglass: typically removed because uneven distribution complicates spray application. Removal cost depends on attic accessibility (low-slope ranches are cheaper to clear than high-pitched cathedrals). Disposal goes to standard construction-debris facilities; not hazardous waste. Cincinnati removal-cost factors: low-slope ranches with full attic access run cheaper to clear ($0.50-$0.75/sqft) than steep-pitched cathedrals or kneewall-restricted attics ($1.00-$1.50/sqft). Disposal goes to standard construction-debris facilities; not hazardous waste. Removal often happens the day before the foam install when the schedule allows it, eliminating one project visit.