Get rid of most of that mulch for starters.........at least move it well away from the trunk.

What kind of tree is it? Is it grafted? Did you plant it or was it done professionally? Where is the root flare in relation to all that mulch?

Oscillating or even automatic sprinkler systems run for a few minutes daily are not going to provide the volume of water a new tree needs. Until the tree is properly established, you need to water deeply and slowly with a hose until the soil is moist to the depth of the rootball. Depending on your climate and soil conditions, that could be daily or it might be every other or every third day. Only you can determine the frequency and duration of the watering schedule by physically testing the soil.

The sucker is not a major concern. Lots of trees produce suckers and for various reasons, Just snap or break it off (better than cutting). The issue here is the proper planting and establishment of the tree, not its ability to produce suckers.

And once you move the mulch, make sure that the root flare is showing. If it isn't, either dig it out or replant the tree properly.

how did you come up with these mysterious numbers .. water until you have provided water at root depth.. and they stop watering until it starts drying down there ... use a hand trowel to dig 3 to 6 inch holes in the gob planted.. and in surrounding soil ... NO ONE can tell you how this all works in our garden ...

but one thing for sure.. broadcast watering will not water down to the root level.. unless ou leave it on for hours ...

where are you ... big city name ..

if i planted a tree n my MI in april or may ... and watered it in properly at planting.. and then mulched .... odds are... i would not need to water until mid to late july.. when the heat of summer starts evaporating moisture at depth ...

NO TREE NEEDS TO be watered every other day ... period ... presuming you are watering properly ...

and dont bother putting it on your new irrigation lines. as once established.. it will ne er need to be watered again .. ever ... its a tree..

and yes.. snip off that lower branch ...im not sure its a sucker .. unless it is coming from below the root flare... and do expose that as noted above ....

https://duckduckgo.com/?t=ffab&q=root+flare&iax=images&ia=images

see primer link.. ken

https://sites.google.com/site/tnarboretum/Home/planting-a-tree-or-shrub

ps: when broadcasting.. leave some bare soil.. so the water can soak into the soil.. and NOT into the mulch alone ... i might wonder if any of you 15 mins of water is getting below the mulch ...

I planted a tree I do have to water every other day. The soil is kind of fast draining. It hasn't rained in months. All weekend it was 105, sunny and windy. This is the first season for the tree and it does need a lot of water right now. Everyone's location is different.

"NO TREE NEEDS TO be watered every other day ... period ... presuming you are watering properly ..."

Absolute generalities like this statement are inaccurate and unrealistic. Every garden is different wrt soil conditions and climate and it is quite possible that daily watering IS necessary for newly planted stock, which should not be allowed to dry out until they become established. In fact most .edu and arboriculture websites strongly suggest daily watering for the first couple of weeks after planting, gradually tapering off to a couple times a week and finally down to once a week or so by the end of the season.

The precise frequency will depend on your soil and your climate!

I don't think that's a root sucker. Looks more like a really low branch growing from the trunk. Which leads me to believe the tree might be planted too deep. Can't say for sure.

When I plant new trees. I water it after planting. I put the end of the hose at the base of the tree and let it run for maybe 3 minutes. Soak the root ball and any surrounding soil. It helps settle the soil and provides a reservoir for the tree to get water from. Once the water in the root ball is diminished, the tree will have an incentive to grow into the moist soil away from the tree. I rarely have to water after that. Only if the leaves are drooping. And if they are, I just repeat the same watering process. My soil is silt and clay. It holds moisture well and also drains. Albeit kind of slowly. So what works for me may not work for you.

ill stand by the comment that if you water properly.. you should need to water every other day ...

under your logic.. no tree would ever successfully seed... as ma nature would not water the tree every other day ...

kid is spot on.. you have to figure it out in your garden.. in your soil ... with your weather ...

ken

What tree do you have planted so close to the house?

"under your logic.. no tree would ever successfully seed... as ma nature would not water the tree every other day ..."

Sorry, but this does not follow logically. The germination and growth of a seed is a vastly different situation than the planting/transplanting of a tree or shrub that is several years old. That should be patently obvious to anyone..........

All of the other comments being valid especial the closeness to the house; the answer to your basic question should you cut off the shoot, the answer is yes. I find it works best to cut of all leave coming from the trunk below the first branch. This keeps the tree focusing on creating good leaves on the branches and growth.

Can you step back and show the entire tree? Very difficult to tell what it is. You appear to have a number of problems. Mulch up next to the trunk not a good idea. Need to have root flare exposed. Need to thoroughly water more often, not shallow watering. Your tree appears to be making a last gasp attempt to live . . . too much mulch over the roots and against the tree is suffocating it.