Certified GKH Gardening Expert
DO NOT use sawdust as a mulch. Sawdust decomposes too quickly and uses all available nitrogen, leaving none for the plants. It would be best to compost the sawdust prior to using it in the garden. Not only will this allow it to age, which will lessen the chances of burning plants, but it will also prevent it from taking up too much nitrogen from the soil. This article might help: https://www.gardeningknowhow.com/composting/ingredients/using-sawdust-in-your-compost-pile.htm
If you have already added them around your plants, I would either remove it or work it into the soil and replace the shavings with straw mulch. This will retain moisture and keep the plants insulated.