Sutak is the period of abstention observed by the Hindus after birth or a death of a family member.
Can we mediate on Lord Shiva with Panchakshari Mantra during Sutak period?
Yes. We can meditate on Lord during Asoucha or Sutak period which generally lasts for 13-15 days depending on region and caste.
Soucham (cleanliness) is needed for works related to God. Like how we need a vehicle (milk or food or water) to carry medicine, rules are needed (followed) for Daiva Pooja (worship). We should worship with Suchi (purity) both internally and externally. Asouchi acquired during death of relatives is called Mrutaasoucha. Asouchi acquired during birth is called Jatahasoucha. Upasana is not allowed during Jatahasoucha and Mrutaasoucha but those who are initiated with a mantra shouldn't stop chanting the mantra. Mantratyaage Daridrataha.
In Asoucha times, we can meditate in mind (mental meditation) without moving lips. There is no dosha for mental meditation during Asoucha days.