Dry the grass clippings on a tarp then store to use in fall. Same with the leaves mow over on a dry day & use your bagger to catch them then put in bags for storage. It's more work, but it does work well. You could try adding more fresh manure to the sawdust in a pile letting it compost into a crumbly brown finished compost before using it on the asparagus.

We've used manures that had the pelleted bedding for horse stalls and guinea pig cages, so basically more sawdust than manure. If piled by itself it's slower, but does darken & break down. If mixed with other ingredients goes faster. We've made hot piles using high nitrogen manures, fresh grass clippings or garden waste, discounted dry cheapest I could find dog food, etc., but not sure if it was worth all the heavy work of turning & tending it. The cold piles do work, but are slow.

One big problem I have found with using just sawdust as mulch is that it packs tightly and water runs off and not into the soil, although the soil underneath always did appear to have ample moisture levels. Usually if I mix some other forms of organic matter into that sawdust then the rain water will flow through and the soil bacteria, evidently now supplied with some protein, digest that sawdust a bit faster then of no other form of OM is mixed in.

I agree with kimmsr. If your sawdust is fine grained. If it's more like shavings (planer shavings or lathe turnings) it will not pack down as much.

Thank you kimmsr & toxcrusadr,
That's the info I was looking far! I can save some leaves & grass to mix in. It seems I always have a better bed when heavily mulched & figured I have a lot of shavings and sawdust
all free stuff. Actually better than free, dumpster cost are ridiculous.
Thanks again
Ed

Mix the dust with compost or grass clipping for a few weeks & you will have a mulch that will hold water & break down, to feed the plants.

I've also mixed the guinea pig + horse manure bedding (mostly sawdust) with used coffee grounds for a darker appearance. When I spread that on about 1" thick last June as mulch in a sunny flower bed it was gone by September.

The pile of it kept moist & covered was only turned as we scooped out from it. After just over a year it's brown & crumbly, but not as dark as my usual yard waste + manures compost. I've used it to mulch densely perennial beds again this year.

Regarding the OP's original question, I would not use a raw sawdust-only mulch on any soil I wanted to plant in. I have seen too many reports of trouble when using woody mulches. I think it should be 'composted' in some manner before using. Wet it, mix it with grass clippings, allow that to 'cook' before applying.

Asparagus seems to be a pretty tough crop. Mine has survived neglect and returned with vigor. I now mulch it with home-made compost and it seems to be pretty happy. I also cover the compost mulch with a grass clipping mulch.

I am starting to wonder about wood mulches. My boss told me he and a friend both had potted tomatoes almost die after using wood mulch in the pots. They pulled it off and the plants recovered.

"Sawdust" runs a wide gamut, as a descriptor.

From green wood, or dry, first of all? From a sawmill, it is fairly green, and from a bandsaw mill, it is also finer than from a circular sawmill. From a woodshop, the wood is seasoned, so the sawdust, shavings and chips are relatively dry and have much fewer microbes in them. A pretty inert material.The dust from bandsaw and cut-off saws is the finest. Tablesaws with ripping blades make more of a fine shaving than dust. Shapers make small chips, as do planers.

Then there is species. Again, a sawmill is generally better, in the eastern half of north america the woods cut are mostly various pines and oaks which break down pretty well and quick. Woodshops tend to use a lot of exotics that do not break down well.

Green white pine dust is a good compost ingredient, and excellent for the composting toilet.